Jean-Pierre Nikolovski
email: jean-pierre.nikolovski@cea.fr

Danièle Fournier

250 DPI at 1000 Hz Acquisition Rate S 0 Lamb Wave Digitizing Pen

est destinée au dépôt

I. Introduction a human-computer interface (HcI) may take various forms. With the advent of portable personal digital assistants (Pdas), smartphones, and tablet Pcs, the traditional keyboard is being replaced by multi-touch or stylus-based input solutions that are perceived as being more user-friendly. The interface is often a transparent plate placed in front of a display [START_REF] Machida | 2-d tactile sensors and tactile sensor arrays[END_REF]. successful touch-and/or pen-based technologies are currently encountered in many hand-held display products. The first hand-held touch technologies such as Pdas were resistive soft films that accepted both finger touch and stylus based interactions [START_REF] Machida | 2-d tactile sensors and tactile sensor arrays[END_REF]. However, this multi-modal input technology must comply with contradictory design constraints requiring both sensitivity to low-pressure touch interactions associated with finger touch and high-pressure interactions coming from point-like forces imposed by passive stylus tips. Its resulting weaknesses are low immunity to scratches and a hardto-avoid force activation threshold that limits detection of light and swift movements. alternately, a method for capacitive sensing of a space-and time-variable physical value such as touch pressure with a network of capacitors was already available almost three decades ago but did not allow precise pen use [START_REF] Nicol | apparatus for the time-dependent measurement of physical quantities[END_REF]. More recently at apple, a surface capacitive network with a charge transfer measuring technique was proposed to develop multi-hand interactions [START_REF] Westerman | Method and apparatus for integrating manual input[END_REF], and with the strong growth of projected capacitive technology, finger touch technologies produce 2-d multi-touch images, often with pre-touch detection [START_REF] Free | Touch location sensing system and method employing sensor data fitting to a predefined curve[END_REF], [START_REF] Hotelling | Multipoint touchscreen[END_REF]. This advantageous feature has already harmed the market share of touch resistive technology. However, multitouch capacitive technology is not the ultimate paradigm and there is still a need for a precise input stylus. In this regard, with its smart inductive stylus and near touch detection, the company Wacom has entered the smartphone market, turning pressure into an additional writing parameter used for example to obtain thicker drawing lines [START_REF] Fukushima | Position indicator, variable capacitor and input device[END_REF]. Multimodal stylus and finger touch detection is a step forward in the development of high-end HcI products. Finger pre-touch localization can be obtained with a projected capacitive technology working at an operating frequency of 250 kHz, whereas cordless stylus pre-touch localization is obtained with an electromagnetic inductive technology operating at a radiating frequency of 500 kHz [START_REF] Sugiyama | Position detection apparatus[END_REF]. Finger pressure measurement can be done with a pressure sensitive sensor such as resistive film, completing a pre-touch and touch capacitive network [START_REF] Yamamoto | Pointer detection apparatus and detection sensor[END_REF]. stylus pressure measurement can be implemented with a flexible variable capacitor C incorporated in the housing of an inductive LC resonant cordless stylus [START_REF] Fukushima | Position pointer, variable capacitor and inputting apparatus[END_REF]. consequently, other non-2-d distribution input devices being developed must exhibit key technical features to remain competitive alternative solutions or at least solutions that can be combined with successful ones. In the acoustic domain, we do not currently see many products that combine both stylus-and finger-based input solutions in a single HcI. In 2002, Ing et al. patented [START_REF] Ing | Method for locating an impact on a surface and device therefor[END_REF] an acoustic cross-correlation process for locating small finger impacts or scratches and producing sensitive objects or display products. Touchless detection and interpretation of proximity movements can also be done by ultrasonic means, as patented by dahl et al. [START_REF] Dahl | acoustic motion determination[END_REF] and Hotelling et al. [START_REF] Hotelling | Proximity detector in handheld device[END_REF].

The oldest acoustic coordinate pen input technologies can be traced back to the 1960s. In 1964, at IbM, Woo [START_REF] Woo | Ultrasonic data converter[END_REF] proposed a synchronous saW digitizing tablet with lucite wedges (duPont corp., Wilmington, dE) to convert longitudinal waves into saWs and a sharp pen tip in the form of a thumb tack. In 1969, Whetstone et al. [START_REF] Whetstone | Graphical data device[END_REF] proposed a stylus with a shock wave that was generated by a capacitor discharge and that propagated in the air medium to two (2-d) or three (3-d) long capacitive microphones located along the edges of the working volume. He considered sonic solutions in solid propagative media as being functionally limited because of the required contact between the tip and the plate and the expensive tuned emitting and receiving crystals. In 1987, Mallicoat proposed a smart stylus graphic input system [START_REF] Mallicoat | Graphic input system[END_REF] for measuring the transit times of in-air ultrasonic signals and an electromagnetic signal used as a means of synchronization. He used only two alternating transmitting transducers at 23 kHz and a stylus incorporating a receiving microphone and an lEd transmitting element. The lEd was used both for time delay measurement and for coding color. The inclination of the stylus is a problem of this measuring principle using air as the propagative medium. It is also a concern for Wacom's inductive stylus. For the air medium, in 1998, Ward et al. [START_REF] Ward | Pen positioning system[END_REF] proposed an ultrasonic stylus with double frequency sources at 40 and 60 kHz superposed in the stylus body to obtain two distance measurements and compensate for the inclination of the stylus.

considering the tablet as the ultrasonic propagation medium, in 1987, adler and desmares improved the rayleigh wave approach [START_REF] Desmares | an economical touch panel using saW absorption[END_REF] by limiting the number of transducers surrounding the panel and replacing them with weighted reflective array strips placed along the panel edges while still maintaining a good signal-to-noise ratio. In 1989, dieulesaint et al. [START_REF] Royer | Touch screen with oscillating loop guided elastic waves[END_REF] proposed a glass touch screen based on an oscillating bulk acoustic wave delay line grid. curiously enough, saW touch technology has been regularly improved over the years with regard to its ability to work with a limited number of transducers operating in some cases with non-orthogonal beams, as demonstrated by Kent [START_REF] Kent | acoustic condition sensor employing a plurality of mutually non-orthogonal waves[END_REF], but in the process has also lost the ability to work with a stylus. This probably results from the application for which saW is usually appropriate, namely point of sales, which does not require a stylus.

Using a tablet as the substrate propagating bulk acoustic waves (baW), on december 30, 1982, Glenn [20] filed a patent for a synchronous ultrasonic stylus with a horn tip and two receiver bars bonded to the side faces of a plate, and hence adapted to the detection of a 0 lamb modes. He proposed measuring the signal amplitude as a means of changing the line width of a drawing. on december 21, 1984, billmann et al. [START_REF] Royer | Elastic wave position sensor[END_REF] filed a patent for a similar tablet which also had a synchronous stylus. In their document, they suggested covering the surface with a lubricating layer such as oil, and topping the stylus vertex with a soft material such as rubber to ease the sliding. both suggestions were also good for reducing some annoying phase inversion aspects related to the inclination of the stylus, although this was not mentioned in the patent. regarding this problem, a few months earlier, on July 25, 1984, sato et al. patented [START_REF] Sato | Tablet type coordinate input apparatus using elastic waves[END_REF] an s 0 lamb wave writing tablet together with a solution to solve the problem of phase inversion at the leading edge of the s 0 lamb mode when an emitting stylus is inclined by adding two layers at the surface of the glass plate or a soft layer covering the tip of the stylus to filter out the mechanical component of vibra-tion responsible for the phase inversion. This problem was also exposed by okada and Inose in a later paper [START_REF] Okada | Phase reversion of the received signal caused by the inclination of the input pen in the ultrasonic tablet and its prevention method[END_REF].

The company canon did also extensive research on a lamb wave writing tablet adapted to the dispersive a 0 lamb mode based on the detection and filtering of the envelope of a long wave packet created by resonance of a horn or conical tip, as presented, for example, in the patent of Kobayashi et al. [START_REF] Kobayashi | coordinate input apparatus[END_REF].

all the vibrating styli found in the literature feature an emitting stylus whose tip vibrates with a movement parallel to the axis of the stylus. With only one key patent on the subject, Hitachi gave up this field rather quickly. at canon, more than 30 Us patents were filed between 1988 and 2002, starting with suzuki et al. in 1988 [START_REF] Tanaka | coordinates input apparatus[END_REF], who designed a writing tablet with three receivers and an axial vibrating tip and a method for detecting the envelope peak of a synchronous a 0 lamb wave packet.

as can be seen from this introduction, lamb wave input styli have been challenged for more than 30 years by strong technical difficulties that call into question the adequacy of the plate as an appropriate means of coordinate measurement. Ultimately, touchless two-handed visionbased input devices such as the one proposed by Malik and laszlo in 2004, which used a camera filming the hands of a user over a table, could be adopted as the cleanest working environment [START_REF] Malik | Visual touchpad: a two-handed gestural input device[END_REF].

In this context, this paper presents a work started in 1991 [START_REF] Nikolovski | lamb waves detection of the (X, y) coordinates of a stylus[END_REF] on a thin s 0 lamb wave pen tablet that could be combined with recent work on acoustic touch technologies such as the amplitude disturbed diffraction method (addP) [START_REF] Liu | Tactile objects based on an amplitude disturbed diffraction pattern method[END_REF], [START_REF] Liu | acoustic wave approach for multi-touch tactile sensing[END_REF], featuring distinct lower operating frequencies in the 10 to 100 kHz range and double-touch capability [START_REF] Nikolovski | system for detecting and locating a disturbance in a medium and corresponding method and computer program[END_REF]. In this scenario, and by analogy with the Wacom approach, the 5-μa low-power pen presented in this paper could get its energy directly from the actively vibrating surface by the piezoelectric effect.

The next sections will present first the operating principle of the tablet and then broadband lamb wave generation and detection efficiency dependency according to the form of the tip and the handling of the stylus. diffraction limitations in burst conditions are investigated, taking into consideration reflection and shear horizontal (sH) conversion at the edges of the plate. The paper is completed with the modeling and experimental measurement of the time difference of arrival (Tdoa) diffraction limits with this type of ultrasonic pen.

II. operating Principle

The (x, y) coordinates are calculated by measuring the time difference of arrival of a wave packet propagating in a glass plate. The emitter is the stylus tip, which incorporates a small source of energy and a piezoelectric transducer that launches burst wave packets that propagate to its vertex at a rate of 1000 bursts per second. Four receiver bars are bonded to the four edges of the plate, as illustrated in Fig. 1(a). The (x, y) coordinates of the stylus are derived from the formula

x t t v y t t v x x s y y s = - = -                         - + - + ( ( ) ) ∆ ∆ ∆ ∆ 0 0 2 2    , (1)
where Δt is the transit time between the stylus vertex and one of the four corresponding receivers, and v s is the lamb wave symmetric s 0 mode velocity. This mode is preferred to the first antisymmetric lamb mode a 0 because it is nondispersive, as can be seen in Fig. 1(b). These two modes are the only ones that can propagate in an isotropic plate of thickness 2h at low frequencies. The important parameters are the transversal and longitudinal wave velocities VT and VL, respectively, Poisson's ratio σ, young's modulus E, and density ρ. one could argue that working with a 0 could be more interesting because of its lower propagation speed and, hence, higher potential resolution; however, as mentioned in the introduction, this path has been explored at canon for more than a decade. also, from (1), we can see that it takes only a 27-MHz clock frequency to reach a resolution of 0.1 mm if the s 0 mode velocity is 5.4 mm/μs, as is the case for a 1-mm-thick b270 glass plate. additionally, acquiring 1000 points/s makes it possible to average the random quantization error and increase the resolution by a factor of three while still operating at 100 points/s. another approach could be to lower the clock frequency to 9 MHz while maintaining the 250 dpi target resolution. Moreover, the low speed of a 0 is not the only important parameter because inaccurate measurements may appear when one writes with swift movements or during inclination or rotation of the stylus about its axis. These errors depend greatly on the vibration properties of the tip, as will be presented in the next section. also, the path chosen by Hitachi or canon with an axial vibration of the tip may not be the best method for efficiently transmitting a broadband mechanical pulse through a point-like touch into the tablet substrate.

III. Vibration Properties of the Tip

To optimize power consumption, the stylus tip must efficiently transfer its vibrating energy to its vertex and from its vertex into a selective lamb mode. In this regard, the profile of the cone plays a key role, as illustrated in Figs. 2 and3. First, if we consider a plane longitudinal wave propagating inside the tip, there are reasons why 1) snell's law of refraction implies mode conversion from longitudinal to transversal waves. 2) For transversal waves, the angle of incidence onto the generatrix of a horn or a cone increases as the number of internal reflections increases [START_REF] Nikolovski | local and selective detection of acoustic waves at the surface of a material[END_REF]. Theoretically off-axis rays launched from a plane base in a direction parallel to the axis never reach the apex and bounce back after several reflections that depend on the aperture of the tip. This is clearly visible on the first echo in tips of various apertures, as illustrated in Fig. 2(a), when a 100-V pulse of width 0.2 μs is applied to a V154-type 2.25-MHz shear wave transducer (Panametrics ndE, Waltham, Ma).

consequently, if most of the energy bounces back before reaching the apex, then lamb wave generation is poor and most of the electrical energy is wasted. Moreover electromechanical impulse response within the tip turns into a long trace, as can be seen with the exponential horn. on the contrary, if the cone aperture is narrow, then most of a shear wave propagating inside the tip reaches the apex and s 0 lamb wave generation efficiency increases. Figs. 2(c) and 3 present one of the best results obtained for s 0 lamb wave generation. Fig. 3 illustrates the fact that the best profile for focusing a plane shear wave so that its focal point is as close as possible to the apex is a long parabolic tip. Fig. 2(c) shows how well the first echo within the tip is attenuated when the apex is in contact with the plate, which indicates good focusing efficiency. The 800-kHz central frequency of the first echo indicates sufficient broadband capability. s 0 lamb wave generation with a parabolic tip reaches 17 Vpp, compared with 1.5 Vpp with a conical tip of half aperture θ = 70°. This result is all the more interesting because the base surface of the cone is about four times larger than that of the parabolic tip. In this setup, the plate is a 71 × 71 × 1 mm b270-type glass with flat polished edges, onto which 70 × 1 × 1.05 mm lead zirconate titanate (PZT) P160 bars from quartz et silice s.a. (courbevoie, France) are bonded with cyanoacrylate glue. The bars are bonded with the poling direction perpendicular to the edge. The parallel central resonance frequency measured in a high-impedance load condition is 1.32 MHz. The series resonance frequency measured in low-impedance conditions is 1.19 MHz. The receiver bar with its transimpedance amplifier is thus optimized for detecting s 0 lamb waves at a central operating frequency of 1.19 MHz. In this regard, the cutoff frequency of the parabolic tip could be increased slightly to optimize emitter-receiver matching. Fig. 3(b) is a picture of a duralumin parabolic tip incorporating a four-PZT piezo-element and a 5-μa solar pulse generator working at a pulse frequency of 1000 Hz.

IV. Inclination/rotation/sliding of the Tip once the tip profile is optimized for efficiently focusing the shear wave at the vertex, the next step is to design a low-cost piezo-element that generates s 0 lamb waves efficiently. This is obtained with a PZT disc comprising two opposite poling areas, as illustrated in Fig. 4. This piezoelement is driven at its radial resonance frequency. This design creates bending waves of the same kind as those obtained with the shear wave V154 type, but at a central frequency of 700 kHz, which is much closer to the receiver bar maximum sensitivity of 1.2 MHz. The next step is to investigate a 0 and s 0 lamb wave properties according to the basic handling operations of the stylus, namely inclination, rotation, and sliding of the tip above the surface.

A. Inclination

In these experiments, the profile of the tip is conical with half aperture θ = 11°. Fig. 4 presents the global behavior with respect to the inclination of a shear wave stylus when the receiver PZT bar is bonded at the surface of the plate and is mainly sensitive to the normal component of displacement. obviously, s 0 lamb mode generation exhibits little dependency on inclination, whereas phase inversion occurs with a 0 and signal amplitude clearly increases.

Fig. 5(a) shows the sensitivity to inclination when the receiver bar is bonded to the edge of the plate and is mostly sensitive to the longitudinal component of vibration. Here again, s 0 is only slightly dependent on the inclination of the stylus. The lamb mode a 0 is not detected, as can be expected; it is known that its longitudinal component changes sign between the upper and the lower mid-thickness of the plate. well-known problem presented in the introduction of s 0 phase inversion already observed at Hitachi. In this configuration, it can be noticed that a 0 is not dependent on inclination. This is, however, not very relevant because a 0 is very dispersive.

B. Rotation

The next handling operation is the rotation of the stylus about its axis. Fig. 6 presents the results for a shear vibrating tip. The receiver bar is bonded to the edge of the plate and is mostly sensitive to the longitudinal s 0 component. as can be seen, the tip behaves as a dipolar source exhibiting a first axis of maximum emission which is perpendicular to the line of separation of half-discs and another axis of zero emission parallel to the same line. This result is obtained with both the Panametric shear 2.25-MHz V154-type transducer and the bipolar PZT disc.

C. Sliding

The last handling operation is the sliding of the duralumin tip over the glass surface toward the receiver bar or away from it. Fig. 7 shows the results for a shear stylus tip. as can be seen, sliding the tip over the dry surface reduces the signal transmission: the top and middle curves correspond to a moving stylus and have slower amplitudes than the bottom curve corresponding to a vertical still stylus. during sliding, friction forces act as a mechanical bias. In this setup, the displacement of the stylus at a speed of a few centimeters per second is comparable to the ultrasonic velocity. Indeed, for a tip vibrating at 1 MHz and a tangential amplitude of 100 Å, the peak vibrating velocity reaches 6 cm/s. Therefore, shear mechanical coupling in sliding conditions, that is, above the friction limit, is dependent on the direction of the ultrasonic vibration of the tip, which produces or alleviates friction forces. 3) There is little dependency on the sliding of the stylus. slight attenuation is noticeable, but the signal waveform is better preserved than the one with a shear wave tip when the stylus is vertical. This result suggests that the coupling stability of the shear wave stylus sliding over the surface should be much better with increased inclination of the stylus, because its vibration ceases to be strictly parallel to the plate.

D. Precessing Tip

considering the results obtained for both types of vibrating tips and axial and bending modes, a stylus tip with a precessing mode of vibration could solve the handling problems. Fig. 9 presents a basic design requiring a unique voltage spike to produce a burst precession. The tip uses a low aperture cone or parabolic profile together with two superposed dipolar PZT discs of diameter 7 mm and thickness 0.2 mm oriented at 90° from each other. on top of the PZT discs is a 1-mm-thick brass disc whose impedance is close to that of the PZT discs. Its purpose is to constitute a resonator for adjusting the spatial phase delay between the discs and to ensure precession.

Fig. 9(a) shows the experimental result of a left-precessing tip for the generation of s 0 lamb mode obtained with a negative voltage spike of 20 V and with a duration of 0.5 μs. The precessing mode radiates ultrasonic energy 360° around. The precessing mode is compatible with the Tdoa operating principle if one receiver is associated with a zero-crossing detection triggered on a positive edge and the opposite one is negative-edge triggered.

E. Pulse Generator

The stylus gets its energy from a small source such as a rechargeable battery placed in its housing. Fig. 10 shows the operating principle of a first-generation 1-ma pulse generator. This small generator is capable of producing 90 V bursts at a central frequency of 1 MHz and a pace of 1 kHz. a second pulse generator is capable of producing double-output 6 V pulses operating in quadrature with only 5 μa of current. This result makes it possible to draw the energy directly from a solar cell.

V. limitations Imposed by diffraction

The operating principle of Fig. 1 is very simple. Piezoceramic bars are bonded to the four edges of the plate, which ensures a flat design, but precision is limited by the diffraction phenomenon in near-field conditions, as illustrated in Fig. 11. This phenomenon results from the spatial extent of the receiver bar, which is several wavelengths long. actually, at 1 MHz, the wavelength of s 0 lamb waves in b270-type glass is 5.4 mm and the receiver bar is 70 mm long. When we move the stylus along a line parallel to the bar, we would like the transit time delay of the wave packet to be constant. In fact this is not true. If the time of arrival of the wave packet is measured at a particular zero crossing of the wave packet, then the higher the order of the zero crossing is, the wider is the cone of integration over the length of the bar. around the plate borders, side reflections on free edges or on PZT-loaded edges also contribute to the building of the received signal. Fig. 11 shows three diffraction diagrams based on the third zero-crossing detection at x = 20, 45, and 80 mm from the receiver bar. one electrode of the PZT bar is bonded to the edge. access to this electrode is ensured by wrapping around the electrode at the extremity of one bar as shown in the picture. This wrapping creates a 6-mmlong non-piezoelectric section of the bar.

In this experiment, the tip of the stylus is sensitive to axial vibrations and is used as a receiver, whereas the bar is the emitter. However, the same diffraction diagram is observed (as long as the elastic wave propagation remains linear) when the stylus is the emitter. The bar is a

A. Modeling of the Diffraction Phenomenon in Semi-Infinite Space

let us recall here a few steps leading to the Kirchhoffsommerfeld formulation of the Huygens-Fresnel principle, stipulating that the diffracted field at r 0 = (x 0 , y 0 ) is obtained by summing circular source waves G(r 0 -r′) centered at r′ = (0, y′) with their amplitude proportional to the field s(r′) in r′.

let us denote by s a solution to the propagation equation in free space for a sinusoidal wave:

∆s k s + = 2 0, (2)
where k is fixed and designates the wave number. let us denote by G the Green's function, the solution of the wave equation in free space in the case of a point source placed in r′:

∆G r r k G r r r r ( ) ( ) ( ), 0 2 0 0 -′ + -′ = - -′ δ ( 3
)
where δ(r 0 -r′) is a dirac distribution defining a point source. The form of G depends on the geometry of the propagating medium. In this study, the s 0 lamb mode features low dispersion and, at 1 MHz, the longitudinal component of displacement is about 5 times larger than the transversal component [START_REF] Dieulesaint | Elastic Waves in Solids 1[END_REF]. This ratio is assumed to be constant over the plate for a given operating frequency and plate thickness. Therefore, beyond the diffuse field, where the s 0 mode is established, the diffraction phenomenon is mostly a two-dimensional problem even though the diffraction diagram may change by a constant value according to the examined plane within the thickness of the plate.

If we look at a problem of cylindrical symmetry, a solution to (2) and ( 3) is of the form [START_REF]Dynamique générale des vibrations[END_REF]

G R AJ kR iN kR AH kR ( ) [ ( ) ( )] ( ), = + = 0 0 0 1 (4)
with r′ = (0, y′), r = (x 0 , y 0 ), R = ( ) ( ); x y y

0 2 0 2
+ ′ -A is a constant; J 0 and N 0 are bessel and neumann functions of order zero; H 0 1 is the Hankel function of the first kind and order zero.

The constant A is calculated using (3) applied to a horizontal disc centered in r′ and of radius a that tends toward zero. In such a case, (3) becomes

∆G k G s a + = ∫∫ 2 1. (5)
solving ( 5) yields [34] A = 1/(4i), where i 2 = -1.

Knowing the value of the mechanical displacement s along the source segment (oy′), the Kirchhoff-sommerfeld formulation can be used to determine s(r 0 ) at any observation point of the plate. combining (2), (3), and (5) we get [START_REF] Jackson | Classical Electrodynamics[END_REF]

s x s y y G R R x R y R x y y L L ( ( , , ) ) ( ) ( ), 0 0 0 0 2 0 2 2 2 2 0 = - ′ ∂ ∂ ⋅ ′ = + ′ - - + ∫ / / d ( 6
)
where L is the length of the bar and the y-axis origin is the middle of the bar. The plane source wave s(x, y) = e ikx has a value of unity at the origin x = 0, and ∂G/∂R = -(

) ( ), k i H kR /4 1 1
where H 1 1 designates the Hankel function of the first kind and order one. We have

s x H y ki kR x R y L L ( , ) ( ) . 0 0 1 1 0 2 2 2 = - ⋅ ′ - + ∫ / / d (7)
If kR ≫ 1 (kR = 6.5 at 1 MHz and for R = 5.5 mm), the Hankel function can be approximated by [START_REF] Stegun | Handbook of Mathematical Function: With Formulas, Graphs, and Mathematical Tables[END_REF] H kR i e e kR kR i ikR 1 1 4

( ) .

( )

→ - ⋅ →∞ -π π / (8)
In a sine wave regime, the diffracted wave at point (x 0 , y 0 ) is then expressed as follows: If we now consider diffraction in burst conditions, we must take into account the transfer function H of the emitter, G of the receiver, and the spectral content E of the drive signal. These functions express the following facts: If we apply a drive signal e(t) to a piezoelectric transducer having an impulse response h(t), we get a mechanical force f(t) described by f(t) = (e * h)(t), where * denotes the convolution product. If this mechanical force is now used as an input to a receiver having an impulse response g(t), we get an output voltage v(t) that can be expressed as v(t) = ((e * h) * g)(t) = (e * h * g)(t).

s x y i i k e R x R y ikR L L ( , ) ( ) . 0 0 0 2 2 2 1 = + ⋅ ′ - + ∫ π / / d (9)
The spectral content V(ω) of the drive signal v(t) is given by its Fourier transform (FT):

V(ω) = FT[v(t)] = v t e t j t ( ) ω - + ∞ ∞ ∫ d = E(ω)H(ω)G(ω). In burst conditions, v(t)
can be expressed in the frequency domain by the general

formula 1 2 / e d ( ( ( ( ) ) ) ) . π ω ω ω ω ω E H G j t - ∞ ∞ - + ∫
Taking into account the diffraction effect, we derive the spatio-temporal estimation of the output signal: v(x 0 , y 0 , t) To optimize computing times, the following assumptions are made: The PZT bar is vibrating in its thickness mode at its central resonance pulsation ω = ω h and the stylus is operating at the radial resonance pulsation of the discs ω = ω g . The output signal v(t) central frequency depends on the ratio q

= 1 2 0 0 / e d ( ( ( ( ) ) ) )( , ) . π ω ω ω ω ω E H G s x y j t - ∞ ∞ - + ∫ by developing s(x 0 , y ), we have v x y t i i E H G k e ik R vt ( , , ) Re ( ) ( ) ( ) ( ) ( ) 0 0 0 2 2 1 1 2 = +      × +∞ - ∫ π π ω ω ω R R x R y v x y t A x y t iB x y L L ⋅ ′      = + - + ∫ 0
= [(E(ω h )H(ω h )G(ω h ))/(E(ω g )H(ω g ) G(ω g ))]
. If this ratio is much larger than unity, then the pseudo-period of the output signal is imposed by the emitter bar, and hence is close to ω h . Inversely, if q ≪ 1, then the pseudo-period of the output signal is imposed by the stylus and is close to ω g . actually, the PZT bar exhibits a strong selectivity because of its free back face and possibly a thickness larger than the plate thickness. Its spectrum H(ω) is consequently approximated by a dirac distribution centered in ω h : H(ω) = h 0 δω h , where h 0 is a constant.

The resonance of the stylus discs is associated with a smaller selectivity (or quality factor) because of the stacking of the three discs and the tip, which requires many epoxy bonding layers, and the mechanical integration of the precessing tip in a housing that will also absorb part of the resonance. because of these conditions, the stylus is assumed to have a broader frequency response than the receiver bar. consequently, the stylus transfer function G(ω) is approximated by a constant G(ω) = g 0 .

as a conclusion, we are naturally placed in conditions where q ≫ 1, that is, where the stylus restores the vibration imposed by the ceramic bar.

now if the drive signal is a voltage spike whose duration is half the pseudo-period of the ceramic bar, we can approximate the spectral content of the drive signal by another constant: E(ω) = e pulse , where e pulse is a constant proportional to the drive amplitude. The impulse response of the output signal then becomes

v t E H G e e h g e i t i t h ( ) ( ) ( ) ( ) Re{ } pulse pulse d = ≈ - -∞ +∞ ∫ 1 2 0 0 π ω ω ω ω π ω ω . . (12)
In the case of a voltage drive step, the tempered distribution associated to the drive signal is

E(ω) = -(e d /i) p.v.(1/ω) + (e d /2)δ
, where e d is the amplitude of the step, δ is the dirac distribution, and p.v. is the cauchy principal value. If we look at the frequencies around the thickness resonance of the PZT bar, the frequency content of the drive step function is approximated by E(ω) = -(e d /(iω)). Then, the output signal v(t) becomes v t e h g e

d h i t h ( ) Im{ }. step ≈ - - 0 0 ω π ω (13)
The output burst diffracted signal v(x 0 , y 0 , t) is then expressed as

v x y t i i e h g k e i v R h pulse pulse / ( , , ) Re ( ) ( )( 0 0 0 0 2 2 1 2 =      + × - π π ω v vt L L R x R y ) - + ∫ ⋅ ′      / / d 2 2 0 (14) v x y t i i e h g k e d h i v R vt h step / ( , , ) Re ( ) ( )( )
0 0 0 0 2 2 1 2 =      + × - π πω ω R R x R y L L - + ∫ ⋅ ′      / / d 2 2 0 . (15)
It can be observed that ( 14) and ( 15) yield the same phase variations. To simplify the expression, the modulus and phase of the diffracted wave are normalized by the modulus and phase of a plane wave which corresponds to the head of the wave packet that is not affected by diffraction. Eqs. ( 14) and ( 15) are normalized by the following plane wave expressions: .

x 0 { } (16)
Eventually, we keep the complex form of the diffracted signal to evaluate the signal peak amplitude. The complex normalized output signal becomes v r (x 0 , y 0 , t):

v x y t k e R x R y P iQ v P r i v R vt x L L r h ( , , ) ( / )( ) 0 0 0 2 2 2 0 = ⋅ ′ = + = + -- - + ∫ ω / / d Q Q v Q P R x y y r 2 0 2 0 2
Phase[ ] arctan

( ) . =         = + ′ - (17)
The phase of ( 17) is equal to the phase distortion of an s 0 plane wave, whereas the modulus of ( 17) is proportional to the peak amplitude of the diffracted wave.

now, let us define the integration cone that takes into account the causality principle which stipulates that the output signal must be zero as long as the wave source r′ considered in the integrand of [START_REF] Desmares | an economical touch panel using saW absorption[END_REF] has not reached the receiver:

R x vt --> 0 0. ( 18
)
We can now simulate various situations corresponding to a finite-length bar excited in burst conditions and radiating in a semi-infinite space. With regard to phase distortion, the measurements are made with reference to a particular zero crossing, which means transit time distortion at constant phase. The modeling is slightly different because we look at phase distortions at constant time delay. This difference is not relevant if we consider that a phase distortion can be linked to the wavefront (i.e., constant phase) by adding an extra time delay Δt to reach a constant or an extra spatial shift Δx to also reach a constant phase. The time delay and spatial shift to reach constant phase (zero crossing) are expressed by

Phase[ ] Phase[ ] , v t v k x r h r h - = - = ω ∆ ∆ 0 0 (19)
which yields

∆ ∆ ∆ t v f x v f v t v r h r h S S = = ⋅ ⋅ = Phase[ ] Phase[ ] . 2 2 0 0 π π (20)
We can now simulate the experiment of Fig. 11. The observation time is 1.5 μs after the arrival time of the head of the wave packet. This is very close to the third zero crossing of the experimental conditions. The simulation is displayed in Fig. 12(a). Experimental measurements are superposed for comparison. as we can see, experimental distortions are a little smoother than the modeling results. This may be explained by the single-frequency approximation. Fig. 12(b) presents the simulation results for two different frequencies at 0.8 MHz and 1.2 MHz. summing the effects, we can imagine that in real conditions, diffraction is smoothed by the bandwidth of the transducers. now, if we consider higher order zero crossing detection and reproduce the same experiment at a distance of 96.5 mm from the PZT bar with zero crossing orders ranging from 1 to 6, we get the graphs shown in Fig. 13. For greater visibility, a constant delay is added to each diffraction diagram so that they can be superposed. as can be seen, by increasing the zero-crossing number, the distortion of the plane wave due to diffraction is also increased. The side effect of the 6-mm non-active PZT extremity resulting from the wrapped electrode is also visible. The symmetrical curves correspond to modeling, whereas uneven ones are experimental measurements.

B. S 0 Side Reflections and SH Conversions

We now take into account in the building of the output signal the possible side reflections of s 0 occurring at the edges of the plate. We have three possible scenarios:

• reflections at the glass-PZT bar interface, • Transmission and back reflections at the PZT bar-air interface, • Possible reflections at free edges of the plate when bars do not cover the entire side length.

We assume here that the frequency•thickness product of the plate is below 1.7 MHz•mm so that high-order symmetric lamb waves are not generated. also taking into consideration the condition of continuity of displacement at the interfaces, we assume that an incident s 0 lamb wave can only be reflected, transmitted, or converted into a shear horizontal (sH) wave. Finally, we assume an incident wave s 0 to be a plane longitudinal wave propagating at s 0 mode speed and a PZT bar to be isotropic in first approximation. The incident wave takes the form s = s 0 e -i(kr-ωt) . For example, the x component of the s 0 reflected wave is written s x rl = s e

x rl i kr t 0 - - ( )
. ω reflection, conversion, and transmission coefficients are defined as

• A rl = reflection coefficient for s 0 ,

• A rt = sH reflected conversion coefficient for s 0 ,

• A tl = Transmission coefficient for s 0 ,

• A tt = sH transmission and conversion coefficient of s 0 . according to the wave polarization defined in Fig. 14, if A rl < 0, there is no phase inversion at the wave reflection.

The method for calculating the reflection and conversion coefficients at free edges consists of writing the continuity of the mechanical displacements s x , s y , and s z and the stresses T x , T y , and T z at the interface. snell's law also applies for incident and reflected waves. at the glass-air interface, the reflection and conversion coefficients are [START_REF] Dieulesaint | Elastic Waves in Solids 1[END_REF]:

A rl i t v v t i t v v l t l t = -( ) + sin[ ]sin[ ] cos [ ] sin[ ]sin[ ] 2 2 2 θ θ θ t rt v v t i i t v A l t l l t v t t i t l v v ( ) = 2 2 2 cos [ ] sin[ ] sin[ ] . θ θ θ with (21)
Fig. 14(a) illustrates the reflection A rl and conversion coefficients A rt according to the incident angle θ i at a free edge of the plate. sH conversion reaches its maximum at around 40°.

The same formalism is carried out to obtain the coefficients A rl , A rt , A tl , and A tt . These coefficients are the solutions of the following system of four equations with four variables:

A A A A A = - + + = 1 t tl tl tt tt A sin[ ] cos[ ] θ θ -                                                            . ( 22
)
based on the solutions of ( 21) and ( 22), we can calculate the reflection coefficient A RL2 corresponding to the steps of a first transmission at the glass-PZT interface described by A tl , then a back-reflection at the PZT-air interface with a coefficient A rtl , and then transmission at the PZT-glass interface with a coefficient A trtl . both A RL1 and A RL2 are displayed in Fig. 14(b) according to the incident angle θ i .

To use the reflection coefficients of longitudinal waves 1 and 2 in the diffraction integrals, we make a polynomial approximation of the fourth and eighth orders, with the variable being the incident angle θ i :

RL i i i i i 1 2 3
as can be observed in Fig. 14 (b), a fair amount of s 0 mode is transmitted in the PZT bar at normal incidence and is then reflected back, whereas for a tangential incidence, most of the s 0 mode is reflected at the glass-bar interface. considering that s 0 lamb wave diffraction near the plate borders involves mainly tangential side reflections, we can conclude that rl2 will contribute little to the diffraction. Incorporating the reflected wave of amplitude rl1, the diffraction integral becomes:

v x y t k e R x R y k e r i v R vt x i v L L h h ( , , ) ( )( ) ( ) 0 0 0 2 2 0 = ⋅ ′ + -- - + ∫ ω ω / / / / d ( ( ) ( ) ( ) arctan R vt x L D L D R x R RL x y y -- - - - - ⋅ ⋅ ′ - { }    ∫ 0 0 0 0 2 2 3 2 2 1 / /       ′ = + = + =         = + dy P iQ v P Q v Q P R x r r , , Phase[ ] arctan , ( 2 2 0 2 y y y ′ -0 2 ) , (25)
where D is the distance between the glass plate corner and the PZT bar limit. Fig. 15 shows the contribution, with D = 0, of the reflected wave of amplitude rl1 to the diffraction pattern at x 0 = 10 mm and second zero-crossing detection. Early detection, within 1.9 μs following arrival time of the head of wave packet, is ensured experimentally by a processing stage that consists of getting the square value of the received signal followed by a double active integration stage [see Fig. 15(a)]. side reflection effects are strong near the edge, where reflections at the glass/PZT bar involve phase inversion of the incident wave.

C. Contribution of the Precessing Tip to the Diffraction Phenomenon

The precession of the tip also brings some distortion to the diffraction effect. actually, if we take a point source at position r′ of the PZT bar, this source undergoes a vectorial projection over the main axes of the stylus discs. consequently, the normalized expression of the Kirchhoffsommerfeld integral taking into account the left-precession of the tip is as follows:

v x y t k R e x R y r i v R vt x L L h ( , , ) cos arctan (
( )( ) 0 0 0 2 2 0 = ⋅ ′ ⋅ -- - + ∫ ω / / / --         - -- >                           y x R vt x c 0 0 0 0 0 ) θ if           + ′ -         -         if i y y x v c h sin arctan ( ) 0 0 0 θ ω ( ( d R vt x y P iQ v r -- >                                  ′ = + + 0 2 0 ) π = = + =         = + ′ - P Q v Q P R x y y r 2 2 0 2 0 2 , Phase[ ] arctan , ( ), (26)
where θ c is the angle between the y-axis and main axis of the lower stylus disk. Fig. 16(a) illustrates the cones of integration in a case of differential detection. a diffraction effect involving side reflections and the precessing stylus angular sensitivity bring more distortion. For simplicity, Fig. 16(b) shows the vectorial projection of the s 0 longitudinal component of displacement over the stylus's main axes when θ c = 0. Fig. 16(c) is a simulation of the differential diffraction effect with a left-or right-precessing stylus in the setup of Fig. 17 and for the case where x = -30 mm. Fig. 17 is an experimental verification of the effect of a left-precessing tip on the precision of the s 0 lamb wave tablet. The dis-tortion brought by the precession is clearly visible and in accordance with the simulation. The horizontal scale is set at 7.2 mm per square. For the vertical scale, a linear offset corresponding to a non-diffracted plane wave is subtracted from the measured value to emphasize the error. The vertical scale is then set at 0.3 mm per square. If we use a single coefficient of linearity, the precision remains within ±0.3 mm, keeping 7 mm margins on all sides, giving an active surface of 57 × 57 mm. additionally, a correction term can be applied to measurements done in the 7 mm margins, based upon the fact that, first, the position error made on the measured value is lower than 1.5 mm, second, the correction term calculated with the diffraction integral using the approximate position is comparable to the one that would be obtained with the real position. Precision can thus be improved or extended to a larger active area. VI. conclusion an s 0 lamb wave digitizing tablet based on deterministic Tdoa localization of a cordless ultrasonic stylus has been presented. The stylus tip is vibrating at 1 MHz in a burst precession mode. This offers a solution to various technical problems associated with the handling of a stylus, namely inclination, rotation, and sliding of the stylus without processing the glass surface. Particular attention has been paid to efficiently focusing ultrasonic energy at the vertex of the tip in the appropriate bending mode to generate nondispersive s 0 lamb waves. This has been obtained with narrow conical tips or thin long parabolic ones. The tips are metallic, but the precession also works with polycarbonate. The power consumption of the stylus is 1 ma at 90 V or 5 μa at 6 V and 1000 pulses/s. The pen can thus be powered by solar cells. The diffraction phenomenon limits the precision of localization to about ±0.3 mm on a 57 × 57 mm region of a 71 × 71 × 1 mm glass plate. The resolution is 0.1 mm at 1000 points/s. This digitizing pen can be merged with a complementary finger touch technology, such as the addP technology, operating in a separate (10 to 100 kHz) frequency range. appendix The following parameters have been used in the simulations of side reflection coefficients rl1 and rl2:

For the PZT P160 bar:

• v l = 2900 m/s, (twice the measured frequency constant), • v t = 1725 m/s (shear horizontal speed of sound in the bar), • ρ = 7300 kg/m 3 (density),

• σ = 0.38 (Poisson's ratio),

• E E 11 = 60 × 10 9 n/m 2 (young's modulus in the plane perpendicular to the axis of polarization of the bar in low electrical impedance loading conditions).

For the b270 glass plate:

Fig. 1 .

 1 Fig. 1. (a) lamb wave digitizing tablet operating principle. (b) s 0 and a 0 lamb mode phase velocities in b270 type glass with VT = 3390 m/s; VL = 5650 m/s; σ = 0.219; E = 71.5 kn/mm 2 ; ρ = 2550 kg/m 3 . Points and squares are experimental measurements.

Fig. 2 .

 2 Fig. 2. s 0 generation efficiency in a glass plate with a duralumin tip. (a) shear wave dispersion versus cone aperture, (b) s 0 generation with a conical tip, and (c) s 0 generation with a parabolic tip.

Fig. 5 (

 5 b) shows the sensitivity to inclination when the stylus tip is vibrating axially. This scenario illustrates the

Fig. 3 .

 3 Fig. 3. (a) Plane shear wave focusing condition. (b) resulting parabolic tip with a 5-μa low-power solar pulse generator. by analogy with Wacom's remote powering, the stylus could retrieve its energy directly from low-frequency waves available at the surface of the plate.

  by comparison, let us look now at an axially vibrating tip. The vibration is imposed by a Panametrics V106-type 2.25-MHz longitudinal transducer. The tip is a duralumin cone with half-aperture angle θ = 11°. The 70 × 1 × 1.05 mm receiver PZT bar (P160 quartz et silice) is bonded to the flat polished edge of a 1-mm-thick b270

Fig. 4 .

 4 Fig. 4. s 0 and a 0 generation dependency on the inclination of the stylus for a shear wave propagating inside the tip and a PZT receiver bar which is mostly sensitive to the normal component of displacement: (a) ±20° inclination, (b) ±70° inclination.

Fig. 5 .

 5 Fig. 5. s 0 and a 0 generation and reception dependency on the inclination of the stylus. (a) a shear wave is propagating inside the tip and the PZT receiver bar is mainly sensitive to the tangential component. (b) a longitudinal wave is propagating inside the tip and the PZT receiver bar is mainly sensitive to the normal component.

Fig. 6 .

 6 Fig. 6. s 0 dependency on the rotation of the stylus: (a) with a V154 2.25 MHz Panametrics shear-type transducer and a lead zirconate titanate receiver bar which is mainly sensitive to the tangential component; (b) with a simple PZT disc (P160, quartz et silice) with alternate poling.

Fig. 8 .

 8 Fig. 8. s 0 tangential component dependency on (a) rotation, (b) inclination, and (c) sliding of the stylus for an axial vibration of the tip.

  little thicker than the previous one. It has the dimensions 70 × 1.3 × 1.4 mm. Its series central frequency is around 900 kHz (and 1 MHz for its parallel resonance visible at high load impedance). The plate dimensions are 200 × 120 × 1 mm.

Fig. 9 .

 9 Fig. 9. (a) Precessing tip design principle. (b) s 0 generation and detection sensitivity to the rotation of the stylus about its axis. The glass plate is 1 mm thick and the dimensions of the PZT piezo-ceramic bar are 70 × 1 × 1.05 mm. Piezo-electric discs are P160 from quartz et silice.

Fig. 10 .

 10 Fig. 10. a 3-mW pulse generator (3 V, 1 ma). a 19-kHz relaxation oscillator triggers 25-V pulses at the T1 collector. The charge pump boosts this peak voltage to a stable 90 V which is further controlled by the microcontroller (μc), which sources and sinks current to the lead zirconate titanate (PZT) discs, thus generating 1-MHz bursts.

Fig. 11 .

 11 Fig. 11. s 0 near-field pulse diffraction diagram for the third zero crossing at various distances from the lead zirconate titanate (PZT) receiver bar between y = 21 mm and y = 93 mm. The stylus is vertical and vibrates axially. The internal electrode of the PZT bar is wrapped around to ease soldering accessibility.

Fig. 12 .

 12 Fig. 12. s 0 near-field pulse diffraction diagram modeling. Experimental conditions are reported in Fig. 11. Modeling in (a) is done at a frequency of 0.94 MHz.

Fig. 13 .

 13 Fig.[START_REF] Woo | Ultrasonic data converter[END_REF]. s 0 near-field high-order zero crossing pulse diffraction diagrams at 96.5 mm from the lead zirconate titanate (PZT) bar (conditions are the same as in Fig.11). symmetrical curves are theoretical results whereas uneven ones are experimental measurements. Modeling is done at the central frequency of the PZT bar: 0.94 MHz.

Fig. 14 .

 14 Fig. 14. (a) reflection and shear horizontal (sH) conversion ratio modeling of s 0 at a free edge of a plate. (b) Front reflection ratio at the glass-PZT interface (arl1), taking into account transmission in the lead zirconate titanate (PZT) bar (arl2). The PZT bar is assumed to be isotropic.

Fig. 18 (

 18 a) shows a sample of handwriting captured with the left-precessing stylus of this study over a b270 glass plate of dimensions 71 × 71 × 1 mm incorporating four PZT bars of dimensions 70 × 1 × 1.05 mm operating at 940 kHz and at an acquisition rate of 1040 points/s. The drawing lines have changes in the gray level every time a stylus lift-off is detected. Fig. 18(b) is a picture of another prototype consisting of a 1.6-mm-thick plate incorporating on each side two bars of dimensions 70 × 1.7 × 1.8 mm and exhibiting an operating frequency of 700 kHz. The stylus incorporates the parabolic tip of Fig. 3.

Fig. 15 .

 15 Fig. 15. contribution of side reflections to the diffraction pattern. (a) second zero detection, 1.9 μs after arrival time of the head of the wave packet. (b) simulation at f = 940 kHz and x 0 = 10 mm with adjacent sides of a corner loaded with lead zirconate titanate (PZT) bars.

Fig. 16 .

 16 Fig. 16. s 0 pulse time difference of arrival (Tdoa) diffraction diagram modeling. (a) Tdoa of contributing ray sources. (b) Vectorial sensitivity of the tip. (c) simulation of precision loss of a right-or a left-precessing tip in the conditions of Fig. 17 where x = -30 mm and y is between -36 and +30 mm.

•

  v l = 5300 m/s (instead of 5650 m/s, which corresponds to an infinite medium), • v t = 3390 m/s (shear horizontal speed of sound), • ρ = 2550 kg/m 3 (density), • σ = 0.219 (Poisson's ratio). acknowledgment The authors are thankful to l. Favro (Wayne state University) for helpful discussions.

  references

Fig. 17 .

 17 Fig.[START_REF] Desmares | an economical touch panel using saW absorption[END_REF]. Precision of the s 0 lamb wave (x, y) digitizing tablet with the left-precessing stylus tip. The stylus is displaced on a set of parallel segments ranging from x = +30 mm to x = -30 mm. Zoom (24 times) on the measured x coordinate around its linear position.

Fig. 18 .

 18 Fig. 18. (a) real-time display at an acquisition rate of 1000 (x, y)/s for (a) a 71 × 71 × 1 mm b270 glass plate equipped with 70 × 1 × 1.05 mm P160 lead zirconate titanate (PZT) bars. (b) Picture of a prototype tablet of twice the dimensions with a parabolic stylus tip (the active area is 130 × 130 × 1.6 mm).

  ). The PZT bar is assumed to be isotropic.

	ρ v	l	( 1	+	A r l	θ 2 )cos[	rt	]	-	ρ A v rt t	θ 2 s in[	rt	]
					=	ρ	v A t l t tl	θ cos[ ] tt 2	+	ρ	v t	t t t	tt A	tt sin[ ] 2 θ
	ρ	t l 2 v v	rl A (	-		i )sin[ ] 1 2 θ	+	rt t A v ρ	c os[ 2 θ	rt	]
					ρ = -	t	t t t l t v v ( )	tl A	tl sin[ ]	t vA t t tt	tt c os[ ]
	rl A (			i )cos[ ]	rt A	sin	rt	tl	tl	tt	θ	tt
			rl							θ	i		rt	θ	rt

Jean-Pierre Nikolovski was born in les Mées, France, in 1967. He received his Ph.d. degree in physics with a major in electronics and acoustics in 1995 from the University Pierre and Marie curie (Paris 6). He is currently a research engineer at cEa, lIsT, where he specializes in acoustic actuators and devices in human-computer interactions and biomedical engineering. He was formerly at EsPcI ParisTech, where he studied and designed several ultrasonic transducers and instruments, such as wideband longitudinal-and shearwave transducers in ndT, surface acoustic wave filters, ultrasonic gas flow meters, ultrasonic digitizing pens for computer graphics, and largearea tap screens. In 1997, he raised capital and co-founded Intelligent Vibrations sa, where, as a chief technical officer, he designed products such as interactive tables and multimodal touch and vocal shop windows based on large-area tap screens. He has authored 21 patents and is the recipient of the Montgolfier Medal from sPI.

Danièle Fournier was born in 1945 in Mauriac, France. she received her Engineer diploma in 1969 from Ecole superieure Industrielle de Physique et de chimie and received her Ph.d. degree in physics in 1979 from the University of Paris XIII. after 40 years of teaching in the University of Paris, she is currently Emeritus Professor at University Pierre and Marie curie (Paris VI). she specialized in applied physics courses (electronics, feedback loops, instrumentation, optics, etc.). she published more than 150 papers in national and international journals and presented her work at more than 60 international meetings with 20 invited papers in optics, instrumentation, and thermal and optical characterization of materials. she has been a member of the international committee of the Photoacoustic and Photothermal Meeting from 1979 to 2011. she has developed numerous international collaborations (berkeley, detroit, nicosia, bochum, campinas, new delhi, etc.).


exposés dans cet article sont issus des réflexions menées à partir d'un projet de recherche porté par Annabelle Boutet et qui s'intitulait BICOOP, des Biens publics aux biens communs, Collaboration, Organisations et Pratiques. (www.marsouin.org/spip.php?article197) 2. Cette question de l'engagement dans des collectifs de production ouverte de connaissance est notam ment poursuivie dans les travaux de Nicolas Jullien et Karine Roudaut dans le cadre d'un projet de recherche ANR CONTINT intitulé CCCP-Prosodie (http://cccp-prosodie.org).

Les enjeux de la numérisation et de l'ouverture d'archives : le point de vue des professionnels L'exemple de la production et la diffusion d'un patrimoine local 1 .

Karine Roudaut*, Annabelle Boutet** L es technologies de l'information et de la communication (sites internet, fora de discussion, wikis, communautés de pratique en ligne, etc.) ont engendré le développement d'outils et de services, de modes de production, de création et de circulation de la connaissance, favorisant des formes de travail collaboratif à distance, l'émergence de collectifs ou encore le partage de répertoires communs. Ces nouvelles situations de travail sont porteuses de mutations socio-organisationnelles comme des formes nouvelles de « knowledge management » (gestion des connaissances) au sein des entreprises, l'engagement dans des communautés de pratiques 2 , le déplacement et le dépassement des frontières organisationnelles traditionnelles.

C'est dans ce contexte de développement des TIC que les organisations publiques -qui ont pour habitude de traiter les informations publiques qu'elles détiennent ou produisent comme des biens enclos (privatisés et mis à disposition de groupes fermés d'usagers) -mettent certains de leurs fonds à disposition du plus grand nombre sur Internet. Cette ouverture se traduit d'abord par la mise en ligne de contenus et induit ensuite la possibilité donnée aux « publics » de participer à leur enrichissement. Ce mouvement d'ouverture des biens publics informationnels au plus grand nombre pose la question générale de savoir comment les professionnels de ces organisations abordent, dans leurs pratiques et leurs représentations, les changements liés à l'introduction des outils et méthodes qui sous-tendent la société de l'information. Ces changements, introduits dans les situations d'activités, impliquent vraisemblablement des transformations dans la production des contenus, les méthodes de travail, la redéfinition des liens sociaux entre les acteurs concernés, tant les professionnels que leurs publics.

Les biens publics informationnels sont définis comme des biens ayant vocation à diffuser ou transmettre de la connaissance (des contenus). Ils sont publics du fait de leur relation forte à la collectivité, ce qui les rend, d'un point de vue naïf mais courant, non susceptibles d'être sujet à une appropriation privée à des fins marchandes. Ce mouvement d'ouverture des contenus comprend donc deux aspects : une mise à disposition des contenus dits publics (ou d'intérêt général) au plus grand nombre, et l'engagement des acteurs concernés dans des démarches collaboratives d'enrichissement de ces contenus. Définissant une autre manière d'exercer les missions publiques en permettant, notamment une plus grande participation citoyenne, cette tendance supporte des enjeux, sociaux, économiques, politiques, juridiques.

Selon nous, les actions portées par le développement des techniques de numérisation dans les métiers de la documentation et de l'archivage publics peuvent être abordées dans une vision de ce qu'est aujourd'hui l'exercice de la démocratie en France, avec les droits, pouvoirs et compétences accordés aux citoyens. En effet, l'administration descendante est chahutée par deux courants : le libéralisme défenseur de la dérégulation en faveur du partenariat ; l'émergence d'une culture citoyenne prônant les bienfaits de l'intelligence collective et de la participation. Ces actions nourrissent des discours autour de la démocratisation par la mise à disposition des citoyens des données publiques ; à ce titre, l'e-administration fait figure de laboratoire d'une standardisation des relations entre les institutions publiques et les citoyens (ou administrés) pour des besoins élémentaires identifiés.

Pour résumer la thèse que nous développerons dans cet article, nous étudierons comment les projets de numérisation d'archives municipales et culturelles [re-]positionnent la notion de démocratisation en suivant trois axes que nous qualifierons de civique, de professionnel et de marchand : (1 : c i v i q u e) la question de mise à disposition pour tous des données dites publiques ; (2 : professionnel) les dispositifs d'appropriation de ces données publiques déployés par les professionnels et les tensions qu'ils génèrent avec d'autres aspects de ces métiers ; (3 : marchand) la dimension économique générée par une situation de plus en plus concurrentielle dans laquelle se trouvent les ins-titutions publiques qui doivent multiplier les actions pour attirer ou générer des ressources, ceci passant par la captation de « publics » nouveaux ou plus nombreux et la preuve de leur utilité publique et politique. Les enjeux de la diffusion et de la numérisation des données publiques : de la conservation à la patrimonialisation des fonds documentaires locaux.

Nous expliquerons dans ce paragraphe comment les décisions et directions politiques en matière de conservation des données publiques conduisent progressivement les acteurs concernés à des démarches de patrimonialisation.

En effet, cette politique d'obligation de mise à disposition des données publiques et de diffusion contient plusieurs enjeux : économiques, relatifs à une mise à disposition de ces données gratuites et/ou à leur marchandisation ; organisationnels et professionnels, en lien avec un élargissement des compétences administratives (organisation) et/ou une transformation du métier d'archiviste ; politiques, autour de la définition des « données essentielles », des modes de définition, des acteurs qui les définissent (experts et/ou citoyennetés).

Les enjeux économiques portent essentiellement sur le choix d'un modèle économique permettant l'accessibilité au plus grand nombre et en même temps la viabilité des dispositifs organisationnels et techniques qui les soutiennent. Les enjeux sociaux portent quant à eux sur les mutations des dispositifs organisationnels et des métiers concernés en termes notamment de missions, de compétences. Le troisième enjeu d'ordre politique est celui de la définition des données dites essentielles, autrement dit les biens qui font l'objet d'un traitement en vue de l'archivage.

De l'obligation de diffusion des données publiques...

Le rapport Mandelkern3 sur la diffusion des données publiques éclaire le contexte sociétal dans lequel s'inscrit notre question. Il pose les bases de tout ce qui suit en matière de diffusion des données publiques par voie numérique. Deux points sont présentés : complétant les droits ouverts aux citoyens en termes « d'accès aux documents administratifs » en 1978 par les lois « informatique et libertés », il défend l'obligation de mettre à disposition les données publiques numérisées, en ajoutant une dimension collective là où on avait jusqu'à présent un accès restreint et individuel. En outre, on attend de l'ouverture aux réseaux numériques mondiaux une incitation à de nouveaux usages, rendus possibles par l'accroissement de la visibilité des contenus français4 .

Une première conséquence est de revoir la manière dont les biens informationnels sont mis à disposition, puisqu'il ne s'agit plus simplement de faciliter l'accès à des requêtes individuelles mais de déployer des dispositifs sociotechniques pour une diffusion au plus grand nombre. La seconde conséquence immédiate est de redéfinir ce qui est proposé à la diffusion, autrement dit les contenus. Comme le souligne le rapport, « l'obligation faite aux services publics de permettre, dans certaines conditions, l'accès aux informations qu'ils détiennent se transforme en une obligation de les diffuser », ce qui nécessite aussi d'assurer « la mise à jour permanente de leur contenu » 5 .

Deux contraintes sont mises en exergue : celui de l'interactivité et celui des modèles économiques pris entre les principes de la gratuité et ceux de la marchandisation. La demande d'interactivité conduit à trois types de conséquences : elle repose sur un nouveau travail de « bornage » des compétences administratives ; elle remet en cause l'organisation interne du diffuseur public ; elle pousse à l'extension de la notion de « données essentielles » 6 .

…à la patrimonialisation des contenus archivés

Si la numérisation soutient l'obligation faite de diffuser les données publiques, elle engendre un effet non prescrit d'élargissement et d'enrichissement des contenus qui, à son tour, produit une injonction à fournir de nouveaux produits. Ainsi, elle contribue à transformer la perception que les professionnels des archives ont ou pourraient avoir de leur rôle et de leurs méthodes de travail, particulièrement pour répondre à la transformation d'une demande d'accès individuelle vers une diffusion de masse. À ce titre, les professionnels des archives ne seraient plus uniquement des conservateurs de biens publics mais des fournisseurs de biens culturels et patrimoniaux.

En effet, jusqu'à présent, en ce qui concerne les professionnels auprès desquels nous avons investigué, la diffusion en réel se faisait, soit par l'intermédiaire de requêtes individuelles sur place, soit grâce à l'organisation d'expositions, soit par le biais de contributions à des expositions (par le prêt de documents d'archives) organisés par des partenaires culturels, des événements comme « Les journées du Patrimoine » ou des rencontres autour d'archives audiovisuelles, etc. Aujourd'hui, les perspectives de diffusion devant un public élargi, ainsi que les enjeux de la concurrence, qui obligent à plus d'efficacité, incitent les professionnels des archives à enrichir leurs fonds, non plus simplement pour répondre à un souci d'historicité mais à des fins culturelles. Par ce processus, les fonds archivés peuvent devenir des biens patrimoniaux utilisés dans la promotion des collectivités locales. Car un des 5. Ibid. p.5. 6. Mandelkern D., 1999 : 33-34. « Les données essentielles seraient alors définies comme les données publiques dont la mise à disposition est une condition indispensable à l'exercice des droits du citoyen, ainsi que de ceux des étrangers résidants sur notre sol. Le critère de la finalité de l'usage commande une présentation des données essentielles sous une forme facilement et universellement accessible ». Voir Mandelkern D., 1999 : 95). La mise à disposition des données essentielles ne peut pas donner lieu à rémunération.

principaux critères de sélection des contenus détenus par les archives locales est la recherche de la proximité et notamment de la proximité géographique. En d'autres termes, on trouve généralement dans les archives des documents se rapportant à des personnalités, lieux, événements locaux et qui sont définis par leur appartenance à un territoire. Rapportés aux terrains que nous avons étudiés, les enjeux sont : ceux de la démocratisation de l'accès aux données et de leur appropriation par tous, ceux de la concurrence pour la conquête de nouvelles ressources et de nouveaux publics, ce qui pose la question de leur visibilité et de leur survie.

Les effets

Les projets de numérisation et d'ouverture des données publiques sont vécus par nos interlocuteurs comme des situations contraignantes associées à une vision techno-centrée plutôt déterministe avec l'obligation de suivre un mouvement irréversible de rationalisation vers toujours plus d'efficacité et d'accélération des temporalités. Pour certains, ils sont imposés par la loi ; pour d'autres, ils relèvent de choix organisationnels ou institutionnels. Loin d'être neutre, la technique, associée à un environnement social et politique de diffusion des données au plus grand nombre, cristallise l'expression d'une tension forte entre un principe citoyen, une logique industrielle, et un modèle marchand.

La mise à disposition des données : un enjeu pour la citoyenneté

Les notions de démocratisation du patrimoine, de diffusion collective et de mise à disposition du plus grand nombre caractérisent une définition de bien commun, entendu comme un bien public dont chaque citoyen peut disposer. Dans les entretiens réalisés, la mise à disposition et la diffusion « pour tous », « au plus grand nombre », prennent la forme de valeurs supérieures érigées en « devoir ». Nous avons en ce sens identifié l'importance que représente traditionnellement l'« obligation de la preuve » dans la mission de conservation par les archives qui vient s'enrichir aujourd'hui de la responsabilité de conserver des traces « pour les générations futures ».

Pour les acteurs interviewés des archives municipales, « être un service public » ouvert aux citoyens passe notamment par une culture de la gratuité. Pour autant, si la démocratisation recouvre une logique de justification de service public citoyen pour les données dites essentielles (Mandelkern, 1999 : 95), la gratuité de tout autre type de données peut être débattue, elle relève d'un choix politique.

L'ambivalence de la numérisation a des effets que nous avons constatés et dont nous pouvons souligner l'interdépendance : la professionnalisation des publics ; la visibilité des agences d'archives ; la concurrence et la marchandisation.

La professionnalisation des publics

La mise à disposition des données au plus grand nombre débouche dans les faits sur une professionnalisation des usagers et une spécification des demandes. En effet, les publics concernés ou intéressés par les archives sont, pour la plupart d'entre eux, des professionnels et des amateurs éclairés. Ce sont, par exemple, les généalogistes, les chercheurs amateurs ou les universitaires, les professionnels de l'audiovisuel. Les métiers des archives y voient une valorisation et une reconnaissance de leur activité portée par la technologie, ce qui renforce leur statut d'expert. L' é l a rgissement du rayonnement et la visibilité des contenus détenus par ces archives permettent un gain de notoriété pour le travail effectué et les compétences développées par les archivistes. Nous retrouvons ici le « mythe Internet » de l'échange déterritorialisé et de la proximité hors les frontières, renforcé par l'idée d'appartenir à une même communauté de pratique autour d'un domaine (les archives), d'une identité et de méthodes. Les professionnels des archives s'ouvrent aussi vers d'autres pratiques d'échange de connaissances, de partage d'informations, de contenus et d'expériences ; en d'autres termes ils développent également de nouvelles formes collaboratives d'exercice de leurs activités, par l'utilisation des services numériques.

Ce processus de démocratisation et d'ouverture reste, dans l'ensemble, partiel car l'accès généralisé n'est pas atteint. Accéder à des contenus numérisés suppose, de fait, un prérequis minimal de familiarisation avec les Technologies de l'Information et de la Communication.

Ce constat justifie la professionnalisation des publics. Le processus de démocratisation que l'on voudrait vertueux produit des effets pervers sous formes de phénomènes d'exclusion ; il existe un hiatus entre des publics susceptibles d'être intéressés par les contenus proposés et des compétences techniques que leur accès impose.

La visibilité des agences d'archives

L' e fficacité et la compétence professionnelle tendent vers le développement d'un mode de fonctionnement plus industriel en lien avec la conservation des données numériques ou dématérialisées. En effet, la conservation de ce type de données offre aux services des archives municipales une nouvelle place au sein de l'administration dans le traitement des questions relatives à l'e-administration et l'archivage électronique. Les professionnels sont maintenant consultés dès « la création même des documents » et n'interviennent plus simplement en « bout de la chaîne ». Nous nous autorisons à dire que les archives ne sont plus « la dernière porte au fond du couloir » mais qu'elles ont ouvert une nouvelle « fenêtre sur cour ». La numérisation contient un enjeu d'image et de valorisation indéniable d'un point de vue org a n i s a t i o n n e l .Le soutien financier apporté dans les projets de numérisation atteste que la préservation de la mémoire n'est plus seulement un enjeu de conservation, domaine réservé des organisations d'archives, mais un espace de luttes pour la définition d'une identité territoriale et la captation des fonds culturels qui la nourrissent.

Concurrence et marchandisation

L'existence d'un débat autour de la mise en oeuvre d'un modèle marchand ressort également des analyses : les questions de la rentabilisation de la conservation des contenus et de leurs modes de diffusion n'ont jamais été aussi vives. L'accumulation des biens dits culturels, si possible rares, entre dans une logique de patrimonialisation. La question des coûts des projets de numérisation de certains fonds, des coûts des supports techniques nécessaires à cette activité, conduit, entre autre, à externaliser la numérisation auprès de cabinets professionnels de généalogistes, à des partenariats avec des entreprises privées et à la recherche de financements externes à la collectivité par le biais des appels d'offre ou de la vente d'images.

Les représentations qui sont associées à ces pratiques ne sont pas nécessairement perçues négativement, et ce malgré l'affirmation d'un principe citoyen. Au contraire, l'enquête souligne que ces pratiques peuvent être valorisées positivement et sont justifiées selon plusieurs registres : soit parce qu'elles représentent un moindre coût pour la collectivité, soit parce qu'elles permettent la viabilité économique de la structure, lorsque celle-ci ne relève pas entièrement du service public, mais doit assurer une part d'autofinancement.

Cette dimension de la concurrence des contenus et de leur marchandisation oriente même parfois les méthodes de travail des archives, particulièrement celles relevant du tri et de l'indexation. Ainsi le tri des biens culturels peut désormais engendrer le refus d'un dépôt justifié par le manque de place ou le coût de la conservation et du stockage. Les critères de l'intérêt et de l'utilité sont évoqués, ce qui pose la question du choix des contenus numérisés et de leur mise à disposition. Tous les points de vue recueillis convergent sur le fait que les documents numérisés et mis en ligne sont ceux qui sont le plus demandés.

Certes, ils invoquent la logique de la conservation pour éviter ou réduire les manipulations qui endommagent, à force de répétition, les documents, mais ils mettent également en avant l'utilité, entendue au sens de l'intérêt économique, de mettre en ligne des documents qui rencontrent trop peu de public. La prise en compte de cet argument, associé à une certaine idée d'appropriation du patrimoine, peut conduire des instances à retravailler d e s documents ou des objets, tels que des films.

Ainsi, les enjeux sont forts autour de deux courants : produire et ven-dre des films thématiques accessibles au plus grand nombre à partir des documents d'origine ou diffuser des documents bruts, tels qu'ils sont produits par les cinéastes amateurs. Ici, les sources de tensions sont liées au fait que l'on s'éloigne, d'une certaine manière, de la conservation comme coeur de métier des archives et de leur identité. Fondamentalement l'enquête permet de montrer que ce n'est pas la diffusion au plus grand nombre via Internet qui pose problème ou pourrait freiner l'engagement vers de tels projets de numérisation et d'ouverture, mais les méthodes d'ouverture de ces données. À ce titre, les sources de tension sont liées à l'analyse ou à la mise à l'épreuve que les professionnels accordent à leurs interactions avec les publics et les données elles-mêmes. Ainsi, garder la maîtrise des données qui sont mises en ligne est une préoccupation forte de la part des professionnels qui s'estiment responsables de la qualité de ce qu'ils offrent.

Cette responsabilité est mise en balance face à la représentation selon laquelle Internet est un vaste espace peu normalisé et qui ouvre une incertitude quant à l'avenir des données publiées. En outre, la responsabilité des professionnels est justifiée par leur expertise et leurs compétences face à des publics dont les ressources en matière de compréhension des données mais aussi en matière de maîtrise des techniques sont questionnées ; les professionnels déplorent ainsi la difficulté qu'il y a d'avoir une démarche pédagogique ou d'accompagnement vers des publics qui ne sont plus accessibles directement mais au contraire mis à distance par la technique. Enfin, ils relèvent l'ambiguïté de la démarche de publicisation liée au fait que, d'une part, cette démarche a une vocation démocratique mais que, d'autre part, elle nécessite une certaine maîtrise technique pour une appropriation sociale du patrimoine ainsi valorisé.

Conclusion

La mise à disposition des données n'est jamais conçue comme une ouverture complète. Les freins identifiés sont de plusieurs types. Il existe une réelle tension face aux conséquences envisagées : tension entre d'une part, l'impression que les missions des archivistes sont réévaluées et d'autre part, l'absence de contrôle des trajectoires des données publiées conduisent à un pillage ou à une dénaturation de ce même travail. Il y a, en effet, tout un travail de conservation, d'indexation qui, s'il est invisible pour l'oeil profane, n'en est pas moins fondamental pour que les archives soient accessibles. Nous retrouvons ici les questionnements relatifs à l'invisibilité du travail et la reconnaissance de l'activité professionnelle. Certains professionnels s'opposent à l'ouverture des données par crainte d'un détournement commercial, par des éditeurs privés, des données publiques, quand les coûts de gestion incombent aux archives. Il en va également de la viabilité économique de structures à économie mixte (ou semi-publiques), dans un contexte global peu enclin à élargir les ressources et les aides. Cette tension des intérêts est adossée à l'affirmation d'une revendication forte de service public. S'y ajoutent des arguments relatifs à l'absence de dispositifs techniques fiables ou de leur coût.

Enfin, les risques d'un détournement des contenus et de non respect des droits liés aux oeuvres et aux auteurs sont récurrents dans ce que génère « le travail de la visibilité ». Dans les discours recueillis, si la modification ou la réutilisation des images est perçue comme légitime, elle ne l'est que tant qu'elle constitue une forme d'appropriation d'un patrimoine avec l'envie de le partager (en le rediffusant). Elle peut alors faire figure de réappropriation. Envisagée de la sorte, elle témoigne d'une attitude plutôt confiante mais sous certaines conditions d'usage : un contexte limité essentiellement au cercle des « proches », réunis dans une communauté de pratique ou au moins d'intérêts, et sans la perspective d'un usage marchand des contenus.

Pour conclure, il est important de souligner que les freins et les facilitations relèvent des mêmes dimensions d'usage. L'exemple le plus net est celui lié à la dimension du travail visible : l'espace virtuel étant aussi un moyen de compenser l'absence de lieu d'exposition et de diffusion propre à ces archives. Ce qui pointe donc une ambivalence sur ce qu'apporte la diffusion des contenus à l'activité des professionnels : entre d'un côté une certaine visibilité, la reconnaissance et la légitimité de leur travail, d'un autre côté l'hétérogénéité et la coopération, mais aussi la concurrence, également du savoir des amateurs, ce qui constitue un des enjeux notamment présents dans les collectifs de production de connaissance ouverte, dont le projet de l'encyclopédie Wikipédia est un exemple emblématique. 

  Comme le montraient déjà Susan Leigh Star et Anselm Strauss 7 , « d'un côté, la visibilité peut signifier 7. Susan Leigh Star & Anselm Strauss (1999), « Layers of Silence, Arenas of Voice : The Ecology of Visible and Invisible Work », Computer Supported Cooperative Work 8: 9-30. la légitimité » ; de l'autre, elle « peut créer une sorte de réification du travail, des possibilités de surveillance » ou de contrôle du travail effectué, « ou encore venir augmenter les charges de travail et la communication ». Elle peut aussi être source d'évaluation, dès lors qu'elle confronte les acteurs aux traces de leur activité 8 . Le deuxième groupe d'arguments est d'ordre économique.

Dans le cadre de ce projet, la méthode de collecte de données adoptée est de type qualitatif à base d'entretiens semi-directifs. Ils ont une durée de cinquante minutes à deux heures. Nous avons rencontré quinze personnes mais les résultats que nous présentons sont produits à partir des discours de trois « praticiens » des archives municipales et communautaires et de trois praticiens de la Cinémathèque de Bretagne. Les entretiens ont permis de dégager les significations des acteurs eux-mêmes à propos de leurs pratiques, de leurs expériences et du sens qu'ils donnent à leurs actions. Au début de ce projet, nous avons posé le postulat que la diffusion des innovations informationnelles et des pratiques qui leur étaient liées relevait d'un processus sociotechnique de type réticulaire, que cette diffusion pouvait dépasser le cadre organisationnel du modèle bureaucratique et impliquait des instances et des individus au-delà des frontières organisationnelles. C'est pourquoi, nous avons adopté l'option de poser le « projet » comme cadre d'intervention et non l'organisation instituée. À ce titre, les dimensions, institutionnelles et individuelles qui ont été investiguées sont les suivantes : l'activité, le travail effectué par l'acteur ; le lien de l'acteur avec le projet (ici la numérisation et l'ouverture des données) ; l'engagement dans le projet en question ; l'état des lieux et les perspectives du projet ; le parcours professionnel.Nous présenterons d'abord le contexte sociopolitique qui cadre cette étude, celui de la diffusion des données publiques et la numérisation du patrimoine, puis les enjeux de la numérisation et de l'ouverture des données (section 2). Enfin, suivra une analyse des effets observés sur les terrains étudiés (section 3).

[START_REF] Mandelkern | Diffusion des données publiques et révolution numérique[END_REF], Diffusion des données publiques et révolution numérique, rapport rédigé à la suite des travaux de l'Atelier présidé par Monsieur Mandelkern au Commissariat au Plan, Paris, La Documentation Française, 124 p.

Mandelkern D., 1999, p. 4.

Béatrice Cahour, Christian Licoppe (2010), « Confrontation aux traces de son activité. Compréhension, développement et régulation de l'agir dans un monde de plus en plus réflexif », Revue d'anthropologie des connaissances, 2, 243-253.

Les développements


Bertrand Langrand

Martin H Siemann

Dieter Kohlgrueber

Advanced FSI computational methods to simulate ditching problems

published or not. The documents may come     Advanced Fluid-Structure Interaction computational methods to simulate ditching problems. From simple guided tests to spacecraft and aircraft structures in full scale

Summary:

Most of air traffic operates over water, airports are mostly located around water, and near-airport operations (such takeoff, final approach, and landing) take place above water. Fortunately emergency landings on water, comprising ditching and crash on water, do not occur frequently. However, as passenger safety under dynamic loads is of key importance in modern aerospace vehicle design, ditching analysis is an important part of the aircraft design. The landing of an airplane on water is an emergency situation that an aircraft faces only once. Loss of the aircraft is acceptable, provided the crew and passengers can safely escape and be rescued. For a water contact to qualify as a ditching, it is necessary that the touchdown follows a prudent approach and acceptable procedures. The design must provide structural integrity to protect all occupants, ensure that no excessive decelerations will be experienced by the occupants, and provide sufficient time for safe egress from a damaged aircraft (FAR 25.801 on Ditching).

In order to quantify the structural capacity of aircraft structures under hydrodynamic loading, the prediction of global and local structural loads and resulting deformations is of fundamental importance. The ditching analysis, however, is very challenging as ditching is a time-dependent, highly nonlinear, multi-physics problem with different length and time scales resulting in complex loading conditions and coupled fluid-structure interaction. The analysis of ditching has been widely based on experimental testing of sub-scale models in order to assess the aircraft motion under various impact conditions with the objective to demonstrate that the aircraft can make a safe landing. Nevertheless, effects related to the structural integrity are rarely regarded in recent experimental campaigns because of the financial and temporal effort associated. Such experiments require costly sub-scale models, limiting the number of designs to be investigated, and they only allow for a certain number of probes, which results in comparatively little insight into involved physical phenomena.

In recent years, simulations are increasingly employed to analyze the structural behavior under ditching conditions. The analysis of ditching can be based on advanced numerical simulations of the transient Fluid-Structure (FS) interaction. Fluid and structure models are coupled with the structural model based on the Finite Element method and the fluid domain based on either the Arbitrary Lagrangian-Eulerian (ALE) or the hybrid Smoothed Particle Hydrodynamics-Finite Element (SPH-FE) approaches. Both computational methods were comprehensively compared using data of guided ditching experiments [START_REF] Siemann | Coupled fluid-structure computational methods for aircraft ditching simulations: comparison of ALE-FE and SPH-FE approaches[END_REF][START_REF] Langrand | Aircraft ditching simulation: a comparative analysis of advanced coupled fluid-structure computational methods[END_REF]. Different test cases were considered for the comparisons, varying the panel thickness and curvature. The numerical results were satisfactory in terms of local pressures, local strains, and global force to consider further applications to full-scale structures.

Advanced FSI computational methods to simulate ditching problems.

Bertrand Langrand NAFEMS France conference -Paris 2018 2

In this communication, these advanced computational methods were applied to spacecraft and aircraft ditching problems in full scale (Figure 1). The water impact of the Apollo Command Module was considered first because experimental data were available in the open literature for different impact conditions (i.e. purely vertical drop tests and oblique (with a significant horizontal velocity component) ditching tests, variation of initial pitch angle, and variation of initial velocities). The numerical results obtained for different impact conditions were very close to the experiment data in terms of accelerations and mean pressure for both computational methods. Furthermore, the ditching of a generic transport aircraft was simulated using both numerical approaches. The generic aircraft model had a quasi-rigid mechanical behavior. The mass, the position of the center of gravity, and the moments of inertia were computed using physical databases. The obtained geometrical and mechanical characteristics of the aircraft model were typical of a short-to medium-range commercial passenger twin-engine jet. Different parameters of the ditching scenario (mass, initial pitch angle, initial horizontal and vertical velocities) were varied to analyze their influence on the impact severity. Additionally, yaw and roll angles were considered in the computations. The influence of the aerodynamic forces (i.e. lift in particular) was studied for some ditching configurations. The aircraft kinematics, velocities, and accelerations obtained with both computational methods were compared.

In addition an approach to consider a deformable fuselage with a realistic mass and stiffness distribution within the ditching simulations will be presented.

Keywords:

Ditching ; CEL-FE ; SPH-FE

Figure 1 .

 1 Figure 1. Full spacecraft/aircraft ditching simulation. Left: ditching of the Appolo Command Module using an ALE approach. Right: Finite Element model of the generic transport aircraft (contour plot: pressure distribution on the generic transport aircraft).