Statistical modal Energy distribution Analysis (SmEdA) can be used to model a fluid-structure problem based on modal information of the uncoupled-subsystems. Recently, the method has been extended to include the effect of a dissipative treatment (i.e. damping or absorbing material). In this paper, SmEdA is tested on a steel plate with/without damping treatment coupled to an acoustic cavity: the numerical result of the energy ratio is compared to experimental one. The data are analyzed for a mid-to-high frequency domain (up to 10 kHz in 1/3 octave band). Both subsystem loss factors are experimentally obtained by a high-resolution modal analysis method based on the ESPRIT algorithm applied to impulse responses of the plate and the cavity. Predicting the energy level requires an accurate estimation of subsystem damping levels. The uncertainty on measured loss factors leads to an uncertainty in the energy ratio depending on min/max damping levels of individual modes in a given frequency band. Once min/max damping levels of subsystems are determined, SmEdA is used to compute the upper and lower limits of the subsystem energy ratio. A comparison with experimental results shows that the measurement data fits in between the SmEdA bounds. In this paper, two types of dissipative treatments are studied: i) a viscoelastic patch on the plate (modeled as an equivalent single layer plate) and ii) a porous material inside the cavity (modeled as an equivalent fluid).

1

Introduction

Statistical modal Energy distribution Analysis (SmEdA) [START_REF] Maxit | Estimation of SEA coupling loss factors using a dual formulation amd FEM modal information, part I: Theory[END_REF] is an effective method to study many coupled problems in a mid-high frequency domain. The method has been recently extended to investigate the influence of an additive damping material applied to a structural subsystem in a plate-cavity coupled problem. The part of the plate treated with a viscoelastic damping pad was modeled as an equivalent property of the plate subsystem [START_REF] Hwang | A methodology for including the effect of a damping treatment in the mid-frequency domain using SmEdA method[END_REF].

In this paper, the focus is on the analogous concept of the equivalent property modeling of an additive damping applied to a cavity subsystem. When a porous material is placed inside an air-filled cavity, it can be integrated into a cavity subsystem as an equivalent fluid. Such modeling greatly reduces the size of the finite element subsystem to be solved thus leads to more efficient SmEdA implementation. At the end, the aim of the study is to investigate the influence of different dissipative materials over subsystem energy flow. Numerically obtained subsystem energy levels and their ratio will be discussed and compared to experimental results.

Since the energy exchange between subsystems is affected by subsystem damping levels, it is important to obtain accurate data. The subsystem damping loss factors are experimentally estimated with the high-resolution modal analysis method based on the ESPRIT algorithm [START_REF] Ege | High-resolution modal analysis[END_REF] from the impulse response of each subsystem. The loss factors are deduced from a number of selected resonant modes in 1/3 octave bands. As damping levels of individual modes can significantly vary within each frequency band, this variation can be used to set limits for a subsystem energy ratio. When minimum and maximum damping levels within a frequency band are considered in SmEdA calculation, they can form upper and lower limits of the cavity-plate energy ratio where experimentally obtained ratio can comply. This gives a deterministic range of an energy ratio for this particular numerical prediction method.

SmEdA method for plate-cavity coupled problems

The SmEdA modal coupling loss factor considers both spectral and spatial coupling of discretized subsystem resonances at a coupling surface. Boundary conditions of each uncoupled subsystem are well defined so that their modal information (resonant frequency and modeshape) is easily extracted with the FEM. In equation 1, 𝛽 𝑝𝑞 12 is the modal coupling loss factor between the plate mode p of subsystem 1 and the cavity mode q of subsystem 2, and 𝑊 𝑝𝑞 12 is the inter-modal work between plate modeshapes and cavity modeshapes. 𝜂 𝑝 1 and 𝜂 𝑞 2 are the damping loss factors

𝛽 𝑝𝑞 12 = 𝑊 𝑝𝑞 12 𝑀 𝑝 1 𝑀 𝑞 2 𝜂 𝑝 1 𝜔 𝑝 1 (𝜔 𝑞 2 ) 2 +𝜂 𝑞 2 𝜔 𝑞 2 (𝜔 𝑝 1 ) 2 [{(𝜔 𝑝 1 ) 2 -(𝜔 𝑝 2 ) 2 } 2 +(𝜂 𝑝 1 𝜔 𝑝 1 +𝜂 𝑞 2 𝜔 𝑞 2 )(𝜂 𝑝 1 𝜔 𝑝 1 (𝜔 𝑞 2 ) 2 )+𝜂 𝑞 2 𝜔 𝑞 2 (𝜔 𝑝 1 ) 2 ]
(1) of the plate mode p of subsystem 1 and the cavity mode q of subsystem 2 respectively. The influence of these two terms on subsystem energy levels are deduced for cases depending on different materials applied to each subsystem: Dimensions of a steel plate and a cavity are 0.5×0.6×0.001 (m) and 0.5×0.6×0.7 (m) respectively. The cavity has five surfaces of the 16 cm thick sold concrete, and its top opening can be covered by a concrete slab of the same thickness. One of the cavity walls has a small hole where microphone cables can be run through. A plate is coupled to a cavity by four metal hinges placed over the plate boundaries and screwed to the top ledges of the cavity.

The dissipative materials are shown in figure 2. The damping pad is a viscoelastic material of a 3 mm thickness. It takes approximately 15 % of the plate surface area. One

Porous material modeling

A porous medium is a material containing pores that are typically filled with liquid or gas. The skeleton portion of the material is called a solid frame in which the sound wave can transmit. If the frame is assumed to be not locally reacting e.g. rigid when a porous material is excited by airborne plane waves, it can be modeled as an equivalent fluid characterized by the fluid bulk properties (characteristic impedance, propagation constant, dynamic density and dynamic compressibility) [START_REF] Bécot | On the use of poroelastic materials for the control of the sound radiated by a cavity backed plate[END_REF] [START_REF] Yaniv | Impedance tube measurement of propagation constant and characteristic impedance of porous material[END_REF]. Such method only corresponds to a treatment on the cavity walls as seen in case (c) of figure 1 e.g. not on or in front of the vibrating plate surface. Equivalent parameters can be deduced from material properties directly measured with an acoustical experiment, which will be given in section 3.2 and 3.3.

The sound propagation inside a porous material is governed by the motion equation and the constitutive law of the medium and is similar to the Helmholtz equation. In equation 2, keq is a wave number of the equivalent fluid,

-𝐾 𝑒𝑞 ∇ 2 𝑝 + 𝜔 2 𝜌 𝑒𝑞 𝐾 𝑒𝑞 = 0 (2)
ρeq is an equivalent density and Keq is an equivalent compressibility. Then the celerity and the characteristic impedance of the equivalent fluid are complex and frequency dependent:

𝑘 𝑒𝑞 = 𝜔 √ 𝜌 𝑒𝑞 /𝐾 𝑒𝑞 (3) 𝑍 𝑐 = √ 𝐾 𝑒𝑞 • 𝜌 𝑒𝑞 (4) 𝑐 𝑒𝑞 = √ 𝐾 𝑒𝑞 /𝜌 𝑒𝑞 (5)
In fact, there are several different equivalent fluid models depending on the expressions of parameters. They normally differ by a number of micro scale parameters such as flow resistivity, porosity, tortuosity, characteristic length, etc. that create bulk properties. Empirical models can give equivalent density and fluid wavenumber and are the simplest since they depend on a single parameter, a flow resistivity (σ). Equation 6and 7 are the Delany-Bazley model and are represented in terms of power law relation:

𝑍 𝑐 = 𝜌𝑐[1 + 0.0571𝑋 -0.754 -𝑗0.087𝑋 -0.732 ] (6) 𝑘 𝑒𝑞 = 𝜔 𝑐 [1 + 0.0978𝑋 -0.7 + 𝑗0.189𝑋 -0.595 )] (7)
where X = ρf/σ is the adimensional number that quantifies the relative importance of inertial effects [START_REF] Dazel | Acoustics of porous materials[END_REF]. Note that the flow resistivity of the porous material needed for the analytical calculation was given by the manufacture.

Two-cavity-method

Bulk properties describe the interaction between material and sound wave and are independent of a material thickness and a size. The characteristic impedance and the propagation constant can be derived from a set of distinctive surface impedance measurements (impedance tube measurement) of a porous material. This can be achieved by changing an air depth behind the porous material. This method is called the "two-cavity-method" proposed by Yaniv [START_REF] Utsuno | Transfer function method for measuring characteristic impedance and propagation constant of porous materials[END_REF] and Utsuno [START_REF] Yaniv | Impedance tube measurement of propagation constant and characteristic impedance of porous material[END_REF].

As seen in figure 3, a sample layer of the porous material is placed inside the impedance tube for measurements of the "two-cavity-method". Arbitrary acoustic impedances behind the porous sample can be achieved by changing an air space depth behind. The acoustic impedance ZS at a reference surface can be related to the characteristic impedance Zc and the propagation constant keq as follows:

𝑍 𝑐 = ±√ 𝑍 𝑎1 𝑍 𝑎2 (𝑍 𝑠1 -𝑍 𝑠2 )-𝑍 𝑠1 𝑍 𝑠2 (𝑍 𝑎𝑖 -𝑍 𝑎2 ) (𝑍 𝑠1 -𝑍 𝑠2 )-(𝑍 𝑎1 +𝑍 𝑎2 ) (8) 𝑘 𝑒𝑞 = 1 2𝑗𝑑 ln ( 𝑍 𝑎1 +𝑍 𝑐 𝑍 𝑎1 -𝑍 𝑐 𝑍 𝑠1 -𝑍 𝑐 𝑍 𝑠1 +𝑍 𝑐 ) (9)
where Za1 and Za2 are the impedance of a closed tube with different air space depths of L1 and L2 respectively, and Zs1 and Zs2 are the reference surface impedances. The impedances of a closed tube are: where 𝜌, c and k are air density, speed of sound and wavenumber respectively.

𝑍 𝑎1 = -𝑗𝜌𝑐 𝑐𝑜𝑡(𝑘𝐿 1 ) (10)
𝑍 𝑎2 = -𝑗𝜌𝑐 𝑐𝑜𝑡(𝑘𝐿 2 ) (11)

Experimental procedure and results

A porous sample with a thickness of 3 cm was cut and placed inside the impedance tube. Following the procedure detailed in [START_REF] Yaniv | Impedance tube measurement of propagation constant and characteristic impedance of porous material[END_REF], Zc and keq were obtained from a set of measured surface impedances (Zs1 and Zs2) and equation 8 and 9. A big tube with a diameter of 10 cm was used to measure Zs1 and Zs2 for frequencies up to 1.6 kHz, and a small tube with a diameter of 3 cm was used for a range from 1.6 kHz to 6.4 kHz. Obtained parameters are shown in figure 4. Note that Zc is normalized with the air impedance (𝜌c).

Once Zc and keq are obtained, the equivalent fluid parameters (ceq and ρeq) can be deduced with equation ( 3), ( 4) and [START_REF] Guyader | Acoustic transmission through orthotropic multilayered plates, part I: Plate vibration modes[END_REF]. The equivalent celerity and density of the porous material are shown in figure 5. Visible transitions after 1.6 kHz seen in both figure 4 and 5 are due to lesser measurement qualities of the small impedance tube. Nevertheless, the empirical Delany-Bazley model is comparable to experimental results. The real parts of the equivalent celerity and density seen in figure 5 are averaged over 1/3 octave bands then used to calculate resonant frequencies and modeshapes in FEM modeling of an uncoupled damped cavity subsystem of case (c).

Subsystem damping loss factor

In order to give more accurate numerical predictions of subsystem energy levels, experimentally estimated subsystem damping levels (η1 and η2) were plugged into equation 1. The damping levels are estimated by the highresolution modal analysis method detailed in [START_REF] Ege | High-resolution modal analysis[END_REF]. The subsystem damping for all three cases in figure 1 was considered: 1) a bare plate, 2) an empty cavity, 3) a plate damped with a single damping pad, 4) a plate damped with two damping pads and 5) a damped cavity. Impulse responses were taken at several locations on the plate subsystem and inside the cavity subsystem then damping levels were estimated and averaged from a number of selected resonant peaks for each 1/3 octave band. In figure 6, damping levels of individual modes for a plate damped with a single damping pad are shown in dots, and an average value is shown in line. Figure 7 shows averaged levels of all five subsystems. The influence of the dissipative materials is apparent. However, two damping pads do not double the loss factors compared to those of a single pad. The levels are approximately twice at low frequencies, and the effect diminishes as frequency increases.

The damping level (η1 and η2) has a direct impact on subsystem energy levels as seen in equation 1. In other words, an accuracy of the SmEdA depends on them. Unless exact damping levels are determined, a numerical prediction is bound to deviate from an experimental result. Suppose that experimentally obtained damping levels are over or under estimated, then upper and lower bounds of the energy ratio (Ecavity/Eplate) can be set by considering the lowest and the highest damping levels in frequency bands. Even if an energy ratio deduced from the average damping levels differs from an experimental result, at least its possible deviation range can be predicted for an engineering purpose. Such results will be given in section 5.

Subsystem energy relation 5.1 Numerical and experimental procedure

SmEdA subsystem energy levels were deduced as the power was injected into a random position on the plate surface. This was done by solving the SmEdA power flow equation [START_REF] Maxit | Estimation of SEA coupling loss factors using a dual formulation amd FEM modal information, part I: Theory[END_REF]. This was also experimentally done as seen in figure 8. As the plate was excited by a stationary harmonic point force (sweep signal), the plate velocity and the cavity pressure were simultaneously measured and averaged over multiple locations in order to give the subsystem energy levels [START_REF] Langhe | Statistical analysis of the power injection method[END_REF]. A frequency range for case (a) and (b) is up to 10 kHz. Note that a frequency range for case (c) is up to the 5 kHz band since the porous material properties measured with the impedance tube are valid until 6.4 kHz.

Result and discussion

Numerically obtained subsystem energy levels for three cases are shown in figure 9. Note that the SmEdA calculations were rendered with average subsystem damping levels. For case (a) and (b), the influence of the damping pad is apparent as seen in figure 9- [START_REF] Maxit | Estimation of SEA coupling loss factors using a dual formulation amd FEM modal information, part I: Theory[END_REF]. A single damping pad diminishes the plate energy levels by an average 7.5 dB compared to (a) at all frequencies. Two damping pads do not give twice the damping loss factor as seen in figure 7-(1). However, its effect is almost doubled in plate subsystem energies as the levels are decreased by an average 4 dB more than a single pad. The cavity energy levels also decrease when dissipative materials are applied to either subsystem. However, changes in acoustic energies are smaller between case (b) and (c) than those in plate energies. The effect of the porous material is also clearly seen in figure 9-(2). The porous material reduces the cavity energies by an average 3.5 dB compared to the empty cavity of case (a). Interestingly, the cavity energy levels are reduced more by treating the plate subsystem than directly treating the cavity at almost all frequencies.

Subsystem energy levels experimentally obtained are presented in figure 10. The plate energies in figure 10-( 1) are in accordance with the numerical results for all cases although the numerical levels are generally overestimated. The differences between plate energies for case (a) and (b) in experimental result are rather small compared to those in numerical result. The same tendencies are shown in the cavity energies as well in figure 10-(2). The SmEdA method can well predict the influence of different damping mechanisms of all three cases but overestimates overall levels.

Figure 11 shows experimentally obtained subsystem energy ratio (Ecavity/Eplate) for case (b) in red solid line, when the plate is treated with two damping pads. The upper numerical limit in black dotted line is given when the The highest damping levels then set the lower limit. Experimental result is within the limits only at high frequencies above 1 kHz. The discrepancies at low frequencies could be due to the coupling mechanism in experimental setup. If the plate boundaries are not ideally clamped, this changes the actual dimension of the plate different from that of the finite element model of an uncoupled plate. Such differences can change a number of plate resonant modes and modal orders which can eventually lead to different spectral and spatial couplings with the cavity modes. Then the amount of energy exchanged through these couplings can deviate from numerical predictions.

Figure 12 shows both numerical and experimental energy ratios for all three cases. The dissipative treatment applied to the plate subsystem alone did not result in substantial change compared to case (a). As seen in figure 12-(1) and 12-(2), both numerical and experimental results of case (b) are comparable for the mid-high domain (above 800 Hz). Since the structural treatment resulted in reduction of both subsystem energy levels as seen in figure 9 and 10, their ratios remain almost unchanged. However, the ratio of case (c) is lower than the rest since only the cavity energies are reduced by the porous material. The ratio of case (c) is approximately 4 dB lower than the rest for both numerical and experimental results. This clearly demonstrates a necessity of the direct acoustic response reduction by an absorbing material if a change in subsystem energy ratio is expected.

Figure 12-(3) shows direct comparisons between numerical and experimental results for case (a) and (c). The numerical predictions are overall comparable to experimental results notably for the mid-high domain. Above 1 kHz, discrepancies between numerical and experimental results are an average 1.7 dB for case (a) and an average 2.2 dB for case (c).

The SmEdA predictions demonstrate overall comparable performance with experimental results for plate-cavity coupled problems. The method can also successfully predict the subsystem energy relation when subsystems are treated with dissipative materials. However, the discrepancies at low frequencies are persistent for all three cases. This could be due to non-ideal boundary condition brought by the coupling mechanism in experimental setup.

Conclusion

A plate-cavity coupled problem is investigated in the framework of SmEdA. When each subsystem is treated with dissipative materials (viscoelastic and porous), they can be modeled as equivalent single layer and equivalent fluid respectively. The equivalent properties of a porous material can be deduced from the simple impedance tube measurement of "two-cavity-method." Obtained parameters are complex and frequency dependent.

It is demonstrated that the dissipative treatments have clear influence over subsystem damping levels as well as subsystem energy levels. However, accurate subsystem damping levels are required for deducing correct energy levels. Otherwise, the energy ratio can be predicted within a range whose upper and lower limits can be set by considering the lowest and the highest damping levels in frequency bands. It is also shown that an energy ratio of the cavity subsystem over the plate subsystem is not significantly modified if only the structural subsystem is treated. This can be achieved by treating the cavity subsystem alone with a porous material.

  (a) a bare plate coupled to a cavity, (b) a plate subsystem partially treated with a viscoelastic layer, (c) a cavity subsystem partially treated with a porous material. All cases are shown in figure 1. All three cases are first numerically modeled then evaluated through laboratory experiments. The case (b) implements the equivalent single layer modeling of a damped plate. A porous material in case (c) is modeled as an equivalent fluid. The methodology and numerical implementation for case (b) are detailed in [2] [4] [5] [6]. Here, the equivalent fluid modeling for case (c) will be emphasized.

Figure 1 . 1 3

 11 Figure 1. Plate-cavity coupled problems for SmEdA analysis: (a) Bare plate coupled to cavity. (b) Damped plate coupled to cavity. (c) Bare plate coupled to damped cavity

Figure 2 .Figure 3 .

 23 Figure 2. Two damping pads attached to a steel plate (left). A porous material inside a cavity (right)

Figure 5 .

 5 Figure 5. Measured and analytical complex equivalent parameters of the porous material. (1) Real part of equivalent celerity. (2) Real part of equivalent density.

Figure 4 .Figure 6 .

 46 Figure 4. Complex equivalent parameters of the porous material. (1) Normalized characteristic impedance. (2) Fluid wavenumber

Figure 7 .

 7 Figure 7. Experimentally estimated subsystem damping loss factors averaged in 1/3 octave band for case (a), (b) and (c). (1) Plate subsystem damping. (2) Cavity subsystem damping.

Figure 8 .

 8 Figure 8. Experimental setup of the plate-cavity coupled structure. Subsystem frequency responses (plate velocity and cavity pressure) are simultaneously measured as the plate is excited. Force and acceleration at the drive point are also measured with an impedance head.

Figure 9 .Figure 10 .

 910 Figure 9. Numerically obtained subsystem energy levels in 1/3 octave bands for case (a), (b) and (c). (1) Plate subsystem energy. (2) Cavity subsystem energy

Acknowledgements

This work was co-funded by the French government (FUI 12 -Fonds Unique Interministériel) and European Union (FEDER -Fonds européen de développement régional ). It was carried out in the framework of the LabEx CeLyA ("Centre Lyonnais d'Acoustique", ANR-10-LABX-60) and the research project CLIC ("City Lightweight Innovative Cab") labelled by LUTB cluster (Lyon Urban Truck and Bus), in partnership with Renault Trucks, Arcelor-Mittal, ACOEM, CITI Technologies, FEMTO-ST (Univ. de Franche-Comté) and LVA (INSA de Lyon).

Références


Ha Dong Hwang
email: hadong.hwang@insa-lyon.fr

Kerem Ege

Laurent Maxit

Nicolas Totaro

Jean-Louis Guyader

Vibrations, Shocks and Noise Equivalent Damping Modeling In the Framework of SmEdA

Keywords: vibroacoustic modeling, Viscoelastic material damping modeling, Porous material damping modeling, Mass reduction for a structure-fluid coupled system

Figure 1. (a) Plate coupled to cavity. (b) Damped plate coupled to cavity. (c) Plate coupled to damped cavity

Introduction

City Lightweight Innovative Cab (project CLIC) aims at developing a new generation of lightweight trucks. Mass reduction of a structural body may necessitate extensive use of additive damping mechanisms. Statistical Modal Energy Distribution Analysis (SmEdA) [START_REF] Maxit | Estimation of SEA coupling loss factors using a dual formulation and FEM modal information, part I: Theory[END_REF] can be used to analyze the energy transmission of a structure-cavity system in the mid-high frequency domain. In this paper, the methodology is extended to take into account the effect of dissipative materials applied to each subsystem. This includes a characterization of the damping material as an equivalent property of treated subsystems, which greatly reduces a size of a finite element system to be solved and leads to a more efficient numerical implementation.

SmEdA Method For Damped Subsystems

The SmEdA modal coupling loss factor considers both spectral and spatial coupling of discretized subsystem resonances at a coupling surface. Boundary conditions of each uncoupled subsystem are well defined so that their modal information (resonant frequency and modeshape) is easily extracted with the FEM. Subsystem energy levels are deduced for cases depending on different materials applied to each subsystem: (a) a bare plate coupled to a cavity, (b) a plate subsystem partially treated with a viscoelastic layer, (c) a cavity subsystem treated with a porous material. All three cases seen in figure 1are first numerically modeled then evaluated through laboratory experiments. The dissipative mechanisms in (b) and (c) are integrated into the subsystem as an equivalent property of the same kind. The part of a plate covered with a viscoelastic layer in (b) can be modeled as an equivalent single layer, and a porous material in (c) can be modeled as an equivalent fluid in an air-filled cavity.

Equivalent single layer modeling of a partially damped plate

An infinite plate covered with a viscoelastic layer can be modeled as a single homogenous layer that gives the same transverse displacements of a multi-layered panel [START_REF] Guyader | Viscoelastic properties of singly layer plate material equivalent to multi-layer composites plate[END_REF]. As frequency dependent nature of a viscoelastic material is considered, an equivalent plate is also characterized by frequency dependent parameters e.g. Young's modulus and damping loss factor. Once such parameters are determined for an infinite plate, the damping loss factors of a partially damped finite plate can be approximated by Modal Strain Energy method (MSE) [START_REF] Koruk | Assesment of the complex eigenvalue and the modal strain energy methods for damping predictions[END_REF] while rendering a finite element calculation. The viscoelastic damping pads seen in figure 2 are applied to a plate at random places, and numerically estimated damping loss factors are compared to those experimentally estimated [START_REF] Hwang | A methodology for including the effect of a damping treatment in the mid-frequency domain using SmEdA method[END_REF].

Equivalent fluid modeling of a partially damped cavity

When a solid frame of a porous material is assumed to be motionless, it can be modeled as a fluid whose parameters are complex and frequency dependent. A fluid phase pressure fluctuation inside a porous material satisfies a standard Helmholtz equation.

In equation 1, is a wave number of the equivalent fluid where ρ eq is an equivalent density, and K eq is an equivalent compressibility. The complex celerity and the characteristic impedance of an equivalent fluid are respectively and . Z eq and k eq of a porous material can be deduced from the impedance tube (Kundt tube) measurement [START_REF] Sellen | Modification de l'impédance de surface d'un matériau par control actif[END_REF]. Once the surface impedance (Z s ) of a porous material is directly measured, all necessary equivalent parameters (Z eq , k eq , c eq and ρ eq ) can be deduced according to the "twocavity-method [START_REF] Utsuno | Transfer function method for measuring characteristic impedance and propagation constant of porous materials[END_REF]." Figure 3 shows the equivalent parameters deduced from impedance tube measurement compared to the empirical equivalent fluid model (Delany & Bazley model) which only needs a flow resistivity of a porous material [START_REF] Dazel | Acoustics of porous materials[END_REF]. A subsystem energy ratio (E cavity /E plate ) is deduced from SmEdA and is compared to experimental results. When a plate subsystem is treated with one or two damping pads ((b) in figure 1), both numerical and experimental results agree on mere change in energy ratio compared to (a) in the mid-high domain (above 800 Hz). This clearly demonstrates that vibratory reduction on the structural subsystem has no significant influence on energy ratio. Numerical and experimental results for case (c) are currently undertaken and will be given in the symposium presentation.

Conclusion

A plate-cavity coupled problem is investigated in the framework of SmEdA. When each subsystem is treated with dissipative materials (viscoelastic and porous), they can be modeled as an equivalent single layer and equivalent fluid respectively. It is shown that energy transmission loss from a structural subsystem to an acoustic subsystem is not significantly modified if only the structural subsystem is treated.

Figure 3 .

 3 Figure 3. Equivalent fluid parameters of a porous material deduced from "two-cavity-method" of impedance tube measurement. (1) Normalized characteristic impedance, (2) Propagation constant, (3) Equivalent celerity, (4) Equivalent density

Figure 2 .Figure 4 .

 24 Figure 2. Steel plate damped with damping pads (left). Equivalent modeling (right)

Acknowledgements

This work was co-funded by the French government (FUI 12 -Fonds Unique Interministériel) and European Union (FEDER -Fonds européen de développement régional ). It was carried out in the framework of the LabEx CeLyA ("Centre Lyonnais d'Acoustique", ANR-10-LABX-60) and the research project CLIC ("City Lightweight Innovative Cab") labelled by LUTB cluster (Lyon Urban Truck and Bus), in partnership with Renault Trucks, Arcelor-Mittal, ACOEM, CITI Technologies, FEMTO-ST (Univ. de Franche-Comté) and LVA (INSA de Lyon).


Philippe Ramirez

Conversions, population movements and ethno-cultural landscape in the Assam-Meghalaya borderlands

Keywords: ethnicity, missions, migrations, epidemics, Assam, Meghalaya, Karbi, Tiwa ------

Conversions, population movements and ethno-cultural landscape in the Assam-Meghalaya borderlands

Our focus area will be the hilly parts of the Assam-Meghalaya borderlands, which correspond to the east of Ri-Bhoi district in Meghalaya and the far western part of the Karbi Anglong district of Assam. The region hosts three main ethnicities: Khasi (or Khasi Bhoi), Karbi and Tiwa, which coincide with three very contrasted cultural entities, in terms of language and kinship, respectively Mon-Khmer and matrilineal, Tibeto-Burman and patrilineal, Tibeto-Burman and ambilineal -although many other features show close resemblances, particularly the ritual and political structures.

Using the examples of a few localities, I will show how current maps of the various cultural, ethnic and religious affiliations, as well as the distribution of the settlements themselves result from close interplay between religious conversions, ethnic conversions and spatial movements.

In the Assam-Meghalaya borderlands, ethnic conversion, by which individuals or groups shift from one ethnicity to another may, in a number of instances, be related to conversion to Christianity. And whether related or not, both these types of conversions are almost always associated with movements in space and the creation of new settlements. How is it that very often in this area, Christianisation is often associated with a change of ethnic identity? [START_REF]On similar phenomena in Nigeria see Harnischfeger[END_REF] Although ethnic conversion in North-East India has been studied very little, the number of cases reported among non-Christian groups leads us to assume that this is an ancient phenomenon or at least that it predates the spread of Christianity. [START_REF]A few mentions of ethnic shifts and conversions may, however, be found about the colonial period: Stack, The Mikirs, 23[END_REF] On the contrary, conversion to Christianity has occurred only within the last one and half centuries, and only within the last century in the Assam-Meghalaya borderlands. Ethnic and Christian conversions are not mutually related by any inherent necessity. I hypothesize that the reason for their concomitance should be sought in the combination of three main factors. First, a general demographical feature: people have been readily and continuously moving over limited distances, forming new villages or settling in existing villages. Then, two seemingly contradictory cultural characteristics, the origin of which we will not discuss here: 1. villages tend to be culturally and ethnically monolithic 2. individuals can easily move from one cultural environment to the other and in the same process from one ethnicity to the other. It should be underlined that such moves happen among rather distinct cultural and social worlds. They do not resume to the adoption of a few minor traits but appear rather as a metamorphosis. No magical transformation is involved though: people generally already possessed some familiarity with the culture they adopted ; however, everything looks as if, within the locality they moved into, their conformity to the local culture and ethnicity became total.

The area was one of the last uplands of North-East India to be affected by Christianisation. [START_REF] Becker | History of the Catholic Missions; Karotemprel, The Catholic Church in Northeast India; Joshi[END_REF] To the south and west, in Pnar and Khasi-dominated zones of Meghalaya, conversions occurred as earlier as the mid-nineteenth century under the Presbyterian Church of India. 7 To the east, in Karbidominated zones, American Baptist missionaries made some attempts from 1859 onwards, though with poor results up until the 1920s. [START_REF] Sangma | [END_REF] For a long period of time, "Bhoi country", i.e. the lower hills north of the Khasi & Jaintia hills, was less of a priority for missionaries: this area was far from Shillong, with a reputation of being inaccessible, its population was looked down upon by uplanders and it had hardly been identified by foreigners. [START_REF]Gurdon was clearly puzzled about who the Bhoi really were[END_REF] German Salvatorians made a brief attempt at penetrating this area in the very first years of the twentieth century. With the outbreak of the First World War, any Germans had to leave; so, the Salvatorians left, having converted only a few villagers. It was only in the 1930s that the Salesians and the Presbyterians took a serious interest in the region. In the 1950s this interest turned into a fierce competition between them, as this area was one of the last to contain a number of "virgin" villages to be converted. [START_REF]On a similar competition in nineteenth-century British Columbia, see Manly[END_REF] Nowadays, the Meghalaya side of the boundary is all Christian except for five Tiwa-speaking villages in the far Northern corner. On the Assam side, the proportion of Christians within the population amounts to almost a half.

Before the advent of Christianity in the area, short-distance migrations were indeed commonplace.

As the Meekirs take up fresh land every two or three years, and remove their dwellings to different parts of the hills, it is necessary to make a new settlement every year with their chiefs. [START_REF] Butler | [END_REF] The two main motives for shifting from one locality to the other were related to agriculture and health. Up until the last decades of the twentieth century, shifting cultivation was by far the main farming method and implied that settlements were displaced whenever fresh land became rare in their proximity. [START_REF] Chattopadhyay | In the nineteenth century, slash and burn was the sole method of farming in northern Meghalaya[END_REF] The second factor mentioned in witness accounts concerns epidemics. Hills were less affected by the plague or malaria than the plains but smallpox and cholera were still rife in the 1950s. The problem of epidemics, as well as unidentified serial deaths, and deaths provoked by uncontrolled deities, was very often addressed by merely shifting settlements. In 1845, Major Butler noted the following about a nearby area, the Mikir hills:

On the appearance of any epidemical disease amongst them, they have recourse to sacrifices; and if the wrath of the deities cannot be appeased -that is, should the sickness not abate -they leave their houses and property, and retire to the densest forests, closing all communication with their former habitations. In the year 1834-35, the cholera raged throughout the Hills, and so alarmed were the inhabitants that there was scarcely a single village that did not remove to a new site. 13 This account from the mid-nineteenth century finds echo in one account we recorded in west Karbi-Anglong:

We left the old village thirty years ago [c. 1980] after three boys died the same day. God Thanasar was angry with us because we hadn't offered a sacrifice to him in the right manner. Maybe there was also an epidemic going on.

Nevertheless, ten houses moved about one kilometre away and settled here, just outside Thanasar's territory. Anyhow, till now, we prefered to carry on the worship.

Another, less common, reason for moving out was the deportation of couples convicted of incest, i.e. of sexual intercourse within the same clan, or of other irregular sexual relationships. Two village polities (Khasi: raid) in Meghalaya, Raid Maiong and Raid Nukhap, just above the Assam plains, illustrate the multiplicity of factors behind the foundation and cultural genesis of settlements, as well as the typical aggregation of local and long-distance immigrants in new settlements. Umlaper village of Raid Nukhap, was founded in the very first years of the twentieth century by an illegitimate Tiwa-speaking couple made up of a man and his wife's elder sister. Both were expelled from the "Old Village" (Kh.:nongbah) of the polity and settled only about three kilometres away. Another "new village", Mawker, was established in the same period by settlers fleeing a smallpox epidemic that had struck the Old Village, also a couple of kilometers away. Ronald 14 recounts the arrival of his family in Raid Maiong: My maternal grandparents were pagans (jyntir). In our native village 6 km away, now in Assam, we used to offer human sacrifices to a local powerful deity (U Blei Wai). After Indian Independence, Assam police undertook to suppress this practice throughout the State. So the sacrificial sword hid by itself deep in the forest. Sacrifices continued for a while in the new place, but people became reluctant to perform them. As a consequence, strange deaths began to occur. My grandparents decided to leave and came here. Before we arrived, Maiong was inhabited mostly by Pnars who were involved in the production of lac. [START_REF]Lac, produced by a tiny insect, Laccifer lacca, has been a prosperous activity in the hills of eastern India. On North-East India, see e.g. Gurdon, The Khasis, 47-48. or Allen, The Khasi and Jaintia Hills, 86. 16 Ramirez[END_REF] When the demand dropped in the forties, most of the Pnars left.

From 1955 onwards, a Presbyterian missionary, Miss Thomas, regularly visited Raid Nukhap and Raid Maiong. She first met with some hostility. Some claim that she cursed villagers for their less than friendly welcome. So when the 1958 smallpox epidemic struck, it was regarded as a sign and therefore massive conversions ensued.

In Raid Maiong and Raid Nukhap, the cultural and ethnic effects of conversion to Christianity have proved rather gradual and, compared to what we will see below, undifferentiated. Obviously, the original differences between Khasi, Pnar, Tiwa and Karbi settlers have seriously faded in favor of a culture that does not apparently differ much from that of other parts of Bhoi country, and which falls within the large Khasi ensemble. Among Presbyterians, non-Khasi languages have died out. As for identity, the Khasi, or more recently the Khasi Bhoi ethnicity has been widely adopted. Surnames are, at first sight, the sole elements which still point to villagers' multiple origins. And even then, surnames have been "translated" into their Khasi equivalents. 16 It may be suggested that, generally speaking, Christianisation has acted as a catalyst for a process that we may call Khasi-isation and which consists in adopting the Khasi language and ethnic identity. The acculturation of Nukhap would be an acculturation to the dominant cultural model in eastern Meghalaya. This is indeed confirmed by the situation of non-Christian Tiwa-speaking communities just a few kilometers away, who seem to have remained totally unaffected by Khasi-isation. Acculturation to the dominant model is, however, significantly reduced among communities living close to the Assam plains and among Catholics: Catholics of Tiwa origin still speak the Tiwa language, assert their Tiwa-ness and are much less prone to refer to themselves as Bhoi. Although some plurality may be found in the origin of dwellers in several villages in the area, there is only one realm in which these villages lack plurality, i.e. their Christian denomination: Catholics and Presbyterian never cohabit, thus all villages host a single denomination. One explanation which immediately springs to mind is obviously the fierce competition between Presbyterian and Catholic missionaries. Yet segregation between Christian denominations is one effect of a more general dynamic which also concerns the separation between Christians and non-Christians.

With the rise in Christian conversions and the establishment of the first Christian villages, deportation became a major cause of spatial displacement. There is a bi-derectional causal relationship between Christian conversions and spatial movements: when new converts were -and still are-banished from villages, and they either founded a new settlement or went to live in already established Christian villages, it may be said that conversion prompted spatial shifts. Predominantly Christian villages from where individuals refusing to convert were driven away fall in the same category, as well as cases of Christians who were thrown out of a Christian village because they did not adhere to the dominant denomination. The causal relationship is somehow the reverse when non-Christians immigrated, whatever the reason, to a Christian village or a mixed village, and as a consequence converted. In this second series of cases, shifts can be said to have provoked conversion. It is this symmetrical causal relationship that we will now demonstrate. Ramirez, CNRS 2014] On the Assam side of the border, segregation is even more visible than on the Meghalaya side. Villages are, with a few exceptions, mono-ethnic, mono-cultural and mono-religious; either all Tiwa, all Karbi or all Khasi, and either Catholic, Presbyterian or "Hindu" -as non-Christian are commonly termed. On both sides of the border, the twentieth century saw a dramatic fragmentation of the human geography. The number of villages increased at least three-fold. Part of this process may be ascribed to the drop in mortality, although the disappearance of epidemics and the availability of medical facilities dates back only to the 1980s in this area. [START_REF]Pre-1960 population data for the hills is subject to caution, and local situations varied greatly, but one may assume a doubling of global human density[END_REF] Yet this does not suffice to account for the highly segregated distribution of settlements that we observe today. The example of Umswai valley gives us clues to the process through which the interplay of epidemics and conversions produced this particular pattern. In the midnineteenth century, Umswai valley's population was concentrated into two large villages: Bormarjong and Amsai. It now hosts 15 distinct settlements. As shown on Table 1, nine of the 13 new settlements are of different Christian denominations, among which seven are Tiwa-speaking and two Karbi. With the exception of the Catholic mission neighbourhood, Tiwas never cohabit with Karbis in the same village. There are very few Khasi-Bhois and Nepalis in the Valley itself but their settlements in neighbouring areas follow the same organizing principles. Pundurimakha village now has a population of about 350, all Tiwaspeaking, Roman Catholic, and they all assert a Tiwa ethnicity. It was set up in the early 1950s as families started to leave the large old Amsai village (present population around 500) to settle a few hundred meters across a rivulet, still within the traditional Amsai territory. Most witness accounts collected today among Pundurimakha's inhabitants involve a series of health-related events which affected the families: Sanjib came with two other related families from Amsai in the early 1960s after several of their children died: "We became ruined. The ojha (Tiwa, Assamese:healer) asked for more and more sacrifices, we could not pay anymore. We thought: 'let's become Christian so we won't have to pay for more.' After a year in Punduri, we were baptised".

Thomas's father was one of Amsai's traditional dignitaries and a firm believer in local deities. In the spring of 1979, the drought caused many cases of dysentry in Amsai which killed his son and daughter. He therefore decided to join his brother who had already settled in Punduri. Thomas describes an atmosphere of panic, phana-phani (Tw.: "everyone dispersed"). And the flights from a disease-stricken village sometimes provoked even more calamities: As it happens, Thomas's father, as the eldest male in the matrilineage (Tw.: jela), was in charge of the lineage god's rituals. After he and his family had left, the lineage god was no longer propitiated and the family relatives who stayed in Amsai experienced even more deaths.

Maladies are not the only physical plight that induced people to move to Pundurimakha. The "fear of mantras", i.e. the fear of spells cast by an opponent in a conflict situation, is also mentioned. Push and pull factors emerged after the Catholic mission was set up in the valley in 1975 and started to offer free schooling and health care. These services were not reserved for Christian villages but convinced many non-Christians that converting and living in Christian villages brought many benefits.

Pundurimakha became a natural refuge for all Amsai inhabitants fleeing calamities, and for wandering groups coming from more distant localities who could not find a proper place to settle for good. Shortly after they arrived, they became Catholics, whether or not they had any previous intention of doing so. [START_REF] As | Matter of Belief[END_REF] And, as in every migratory movement, networks of acquaintance and kin played a central role.

Mathew's young brother was only five when he started to suffer badly from fever (Tw.: lungjawa, later diagnosed as malaria). Traditional remedies had no effect. After it was discovered that birds had eaten away a piece of the child's ear, the family became seriously alarmed. A distant relative from Punduri, where their maternal uncle used to live, persuaded them to come and settle there. He promised that the child would recover and that they would not have to spend any more money on sacrifices.

As mentioned earlier, flight before epidemics and similar calamities was nothing new. The new factor in the Assam-Meghalaya foothills from the 1920s onwards was the intermingling of "health refugees" with "religious refugees" -to use modern terms. Those who fled epidemics and took refuge in makeshift settlements increasingly met those who had been expelled after converting.

"Religious refugees" cover a variety of cases. As on the Meghalaya side, during an initial period, the greatest number was made up of new converts to Christianity who had been expelled from non-Christian villages. After Christian villages had been set up, those who refused to convert were in turn expelled. In essence, all these situations stem from a principle of total separation, where only one religious affiliation is tolerated in a locality. Thus, converting meant -and still means -moving in the short term, and in return moving into a village where the community follows a different creed meant converting in the short term.

We came to save ourselves from fever. But one could not just come here and stay without converting.

And this could lead to situations where, over their lifetime, people would change places and denominations several times over.

That family came with us here and converted. After a while they changed their mind, went back to our original village and re-became pagans.

Comparatively speaking, Pundurimakha represents a "simple" situation because the integration of newcomers involved a change of religion but not of ethnicity. Our third example illustrates how even more erratic the paths of individuals caught in the dynamics of separation could/can be and, in a sense, how unproblematical repeated shifts in religion and ethnicity might be.

Roman Marjong village (pop. 300), in Umswai valley, is a remarkable example of the multifarious connections between Christian conversion, ethnic shifts and spatial mobility. Like many villages in the surrounding area (e.g. Pucari Hindu/Pucari Kristian), Roman Marjong is named after the religious affiliation of its inhabitants, i.e. Roman Catholic, therefore meaning "the Catholic part of Marjong", in contrast to Bormarjong, "Big Marjong". While Bormarjong is only Tiwa speaking and a "Hindu" village (pop. 700), Roman Marjong is not only Catholic but Karbi speaking and most of its inhabitants have Karbi surnames. Roman Marjong's existence goes back to the very first Christian incursions in Umswai valley. According to our informants, it was founded by Catholics in 1914. Missionary sources confirm that the first converts were six "Karbis from Marjong" who came to be baptized by the Salvatorians in 1914. 19 However the very first inhabitants of Roman Marjong might not all have been Christians; they might have come for some other reason, and perhaps before 1914. B.K. Gohain reports that the village was founded by incestuous couples expelled from Bormarjong, the largest Tiwa-speaking village. 20 Villagers today attribute the foundation of Roman Marjong to five or six Christian families who had been expelled from Bormarjong. They settled for a while very close to the original village, in a place called Sakrapera (Figure 3). Shortly afterwards, some individuals preferred to abandon Christianity, they re-converted to "Hindu" and went back to live in Bormarjong. Others were converted by Presbyterians from Pucari Kristian and went to settle in that locality, an hour's walk away towards the northeast.

Figure 3 Origins of a Roman Marjong's couple. © [Ph. Ramirez, CNRS 2014] Among the handful of Bormarjong converts who remained Catholic was Lili Amsong and her brother, Lang. Lili's husband, Sondar Madar -who married her matrilocally -refused to convert. Their story was told to me by their grandson Robert Teron, now in his early forties. Around 1935, his grandparents and great-uncle left Bormarjong and settled in Roman Marjong. The small village must have already been Karbi dominated because shortly after their arrival, they were adopted into Karbi clans: the sister and brother became Teron, the husband became Be. These clans were neither chosen randomly, nor on the basis of their friends' nor according to their personal preferences. They corresponded to the Karbi clans that were equivalent to their original Tiwa clans. Thus Teron is said to be "similar" to Amsong, and Be to Madar. These equivalences between surnames, which amount to equivalences between descent groups, are commonly found in the Assam-Meghalaya borderlands and imply relations of exogamy among equivalent descent groups across three different ethnicities: Karbi, Tiwa and Khasi. People who have equivalent surnames are said to be "the same" and therefore cannot marry. [START_REF] Ramirez | Ethnic Conversions and Transethnic Descent Groups". On similar phenomena in Nagaland, see Hutton[END_REF] Going back to the story, while Lili and her husband became Karbi but remained Catholic, Lang, Lili's brother, soon went to live in Pucari Kristian, where he had a Karbi ceremonial friend (As.: sugi) and became a Presbyterian Karbi. After Lili died, her husband lost his mind and left for Bangladesh before returning to another area of Karbi-Anglong. Their son Cornelius Teron married a Roman Marjong girl, Martha Phangchopi, who was originally a Tiwa from Bormarjong. Martha's mother, Elizabeth, had converted to "Catholic" but her first husband refused to do so and all her kin were opposed to the idea. She therefore left home with her daughter and went to Roman Marjong. There she married Laisingh Phangcho, who my informant confessed not remembering whether he was an original Karbi or a Tiwa converted to Karbi-a very revealing irresolution indeed. As is common among Karbis in cases of remarriages, Martha's daughter took her stepfather's clan. Soon after the birth of my informant, Robert, i.e. in the early 1970s, his parents died. Robert went to live with Grand-Uncle Lang in Pucari and, although a Catholic "by birth", he was educated as a Presbyterian. Robert told me that up until a very late age he had not at all suspected that his grandparents on both sides had been Tiwa. Everybody around him only spoke Karbi and it was later in life that he learned Tiwa from his maternal grandmother. On becoming an adult, Robert came down to Roman Marjong to take care of his parents' house and land. He thus "reconverted" to "Catholic". He then married a "Hindu-born" Tiwa girl from Bormarjong, Jonaki Malang. Jonaki became Catholic but refused to take a Karbi surname, a choice now more and more common.

All Roman Marjong villagers except two bear Karbi surnames. Some are recognized as "original Karbis". Others, it is recalled, descended from Tiwa parents or grandparents. They are generally referred to by their Karbi surname but it may happen that their former Tiwa title is used, especially in Tiwa speaking situations. In Roman Marjong, adoption into a Karbi clan is relatively simple. People are adopted by a lineage belonging to a clan that is equivalent to their Tiwa clan. The convert goes to meet an elderly male member of the lineage who "ties a cotton thread" (Karbi: hongjenkekok) around their right wrist and offers them some food. The wife of the elder offers the adoptee some milk. In Karbi-dominated areas further east, conversion procedures are generally more elaborate, particularly when an alien is concerned. [START_REF]For details see Ramirez[END_REF] Converting a non-Karbi does not, however, differ in principle from bringing a Karbi into a new lineage or clan, or even making a newborn baby a member of the lineage. All these procedures fundamentally amount to adoption into the descent group through "purification" (Kb.: kapangthir). The difference is that in the case of a non-Karbi, purification and rites de passage are more elaborate, as higher risks are involved.

The case of Roman Marjong provides valuable insight into the complexity of the interactions between population movements and the ethno-cultural genesis of present settlements. Roman Marjong's current cultural and ethnic features did not result from a linear, insulated process by which a core group of founders grew locally to become the Karbi Catholic village we know today. These features resulted from continuous geographical, ethnic and confessional mixing in the area. The history of Roman Marjong cannot be understood without taking into account the multiple movements of individuals throughout the twentieth century, their shifts back and forth, their religious and cultural mutations. Hesitancies and oscillations are key aspects for understanding how the village has evolved. These hesitancies pertained to various tensions at family level, e.g. about matrimonial choices, or at village level, e.g. between religious affiliations (Catholic / Presbyterian / Hindu). In all these cases, individuals showed an amazing propensity to move. And, as in the Amsai-Pundurimakha scenarios, this was facilitated by and achieved through networks of acquaintances in neighboring settlements.

The cases of village genesis described here are representative of pervasive general processes, but are far from summing up the particular features of all localities. This is a key aspect of the anthropological complexity of regions like the Assam-Meghalaya borderlands. Relatively similar initial conditions result in very different social formations. The most common scenario is the one we described for Roman Marjong and Pundurimakha, where a series of individual events finally led to a strong linguistic, ethnic and religious coherence. These can be firstly contrasted with villages which have not crystallized into mono-ethnic entities. One example is Umkashi where a Salesian mission was setup in 1945 and which hosts 34 Karbi households, 20 Tiwa, 11 Pnar and 15 Khasi Bhoi. Most are Catholic but two pagan households (Kh. jyntir) are still to be found there. And different again are communities who converted collectively and suddenly. All the inhabitants of Trairit "Model Village", which was formerly Tiwa and surrounded by large Tiwa villages, joined the Presbyterian Church collectively on the initiative of Karbi catechists and shortly after that, they all adopted Karbi names. [START_REF]Collective conversions are not exclusive to religious conversions. The most striking example I have recorded is that of a hamlet very close to Guwahati, where a few years ago a dozen families formerly assuming a Bodo ethnicity converted as one man to Karbi ethnicity[END_REF] The scant ethnographic data presented here lead to several immediate observations. First, the cultural landscapes of North-East India cannot be analyzed properly without taking into account the importance of mobility, and more especially of short-distance local mobility, the "micromigrations" described by Toni Huber for Northern Arunachal. 24 Ancient and long-distance migrations may be of some interest but -even when related to real events -do not teach us much about the actual processes of cultural and ethnic genesis and changes. In contrast to the canonical image of tribes travelling as one man and bringing their culture from far away to shape their new homeland -an image common in modern folk histories, we have seen individuals and small groups moving to the next locality and adopting the local dominant culture.

Second, the range of ethnic shifts I have presented obviously partly owes to the advent of missionary Christianism in the region. However, changes of ethnicity were made possible by institutions or at least social features which predated Christian conversions. Among these is the mere possibility of ethnic change and the patronymic equivalence system which enabled the pursuance of clanic relationships despite reinforcement of ethnic boundaries.

Another important point is that conformity to the dominant cultural and ethnic patterns of the village seems to prevail over the perpetuation of those inherited from the lineage. This does not put into question the primacy of descent over ethnicity in terms of long-term membership, quite the opposite indeed: people move from one ethnicity to the other while remaining attached to the same descent groups. Nevertheless, whether conformity is voluntary or imposed, most newcomers to a village will soon adopt the village's language at home and readily convert to the village ethnicity. And in the same manner they will, if it has not already been done, adopt the religious denomination prevalent there. This does not preclude the possibility that after a few years the same persons or their descendants will suddenly move to another settlement and easily adapt to its particular setup. Plurilingualism, i.e. competence in several languages, is definitely an asset in this context. While villages show a strong linguistic distinctiveness, their inhabitants are often fluent in the languages spoken in the surrounding area. I think that in the same manner we might suggest that their pluriculturalism helps them to evolve across a multicultural landscape. This might help to understand how despite continuous spatial movements, North-East India did not turn out into an evenly mixed melting-pot, but into a relatively compartmentalised one, ethnically and culturally. We saw how new inputs are either incorporated into existing compartments or contribute to the creation of new compartments according to the same logic of exclusivity. It is this latter process which happened after Christianity was introduced in the Assam-Meghalaya foothills.

The processes put into light here obviously open up to crucial questions about the cultural history of North-East India as well as of areas where similar phenomena have been documented. 25 Ethnic shifts may at first glance sustain the idea that present ethnicities had been invented. Obviously, all the ethnic groups we know today might not have resulted from a very long biological continuity. 26 But even if we assume that present ethnicisation resulted from identity polarisations congealed during and after the colonial period, it does not imply that, prior to that, the region was culturally undifferenciated. People probably did not identify to categories hierarchically superior to clans, like present-day tribes, but conformed to local cultures that differentiated at the village level.

Figure 1

 1 Figure 1 Area of Study. © [Ph.Ramirez, CNRS 2013]

Figure 2

 2 Figure 2 Umswai valley villages ,1867-2010. © [Ph. Ramirez, CNRS 2014]

Table 1

 1 Languages and religious denomination in Umswai valley villages

	VILLAGE	LANGUAGE	RELIGION
	Amchabra	Tiwa	Catholic
	Arlang Luri	Tiwa	Catholic
	Chikda Makha	Tiwa	Catholic
	Punduri Makha	Tiwa	Catholic
	Thaulau	Tiwa	Catholic
	Amkhalam	Tiwa	Hindu
	Bormarjong	Tiwa	Hindu
	Satpani	Tiwa	Hindu
	Umswai Lalung	Tiwa	Hindu
	Mawlen	Tiwa	Presbyterian
	Umcetri	Tiwa	Presbyterian
	Karbi Hidi	Karbi	Hindu
	Rapadang	Karbi	Hindu
	Maikramca	Karbi	Presbyterian
	Umswai School	Karbi	Presbyterian

The study undertaken byLangstieh et al., "Genetic Diversity and Relationships." has shown that people who presently identify themselves as Khasi and Garo are genetically hardly distinct.