Publications

2006

• Second-order theory for nonlinear composites and application to isotropic constituents
  
  • Idiart Martín I
  • Danas Kostas
  • Ponte Castañeda Pedro
  Comptes Rendus. Mécanique, Académie des sciences (Paris), 2006, 334 (10), pp.575-581. New prescriptions are proposed for the ‘reference’ fields in the context of the ‘second-order’ nonlinear homogenization method [P. Ponte Castañeda, Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory, J. Mech. Phys. Solids 50 (2002) 737–757], and are used to generate estimates for the effective behavior and first moments of the local fields in nonlinear composites. The new prescriptions yield simple, analytical expressions not only for the effective potentials, but also for the macroscopic stress-strain relation, as well as for the phase averages of the strain and stress fields. For illustrative purposes, ‘second-order’ estimates of the Hashin–Shtrikman type are provided for two-phase, transversely-isotropic composites with power-law phases, and are compared with exact results available for power-law, multiple-rank, sequential laminates. The agreement is found to be quite good for all ranges of nonlinearities and inclusion concentrations considered. (10.1016/j.crme.2006.06.006)
  DOI : 10.1016/j.crme.2006.06.006
• Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering
  
  • Nemitz Nicolas
  • Bonnet Marc
  , 2006. This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving the free field and an adjoint field associated with the cost function. These fields are computed by means of a boundary element formulation accelerated by the fast multipole method. A computationally fast approach for performing a global preliminary search based on the available overspecified boundary data is thus defined. Its usefulness is demonstrated through results of numerical experiments on the qualitative identification of hard obstacles in a bounded 3D acoustic domain, for configurations featuring nodal unknowns and sampling points, based on exact or noisy synthetic data. (10.1016/j.enganabound.2007.02.006)
  DOI : 10.1016/j.enganabound.2007.02.006
• TGV disc brake squeal
  
  • Lorang Xavier
  • Foy-Margiocchi Florence
  • Son Nguyen Quoc
  • Gautier Pierre-Etienne
  Journal of Sound and Vibration, Elsevier, 2006, 293, pp.735-746. The discomfort generated by the noise emission of braking systems in train has aroused recently many studies on the mechanical modeling of brake noise in France. A theoretical and numerical discussion on the phenomenon of brake squeal is given here in relation with some experimental data. This study is based upon a flutter instability analysis giving the unstable modes of the TGV brake system. (10.1016/j.jsv.2005.12.006)
  DOI : 10.1016/j.jsv.2005.12.006
• A transformation of elastic boundary value problems with application to anisotropic behavior
  
  • Pouya Ahmad
  • Zaoui André
  International Journal of Solids and Structures, Elsevier, 2006, 43, pp.4937-4956. A general geometrical transformation of the coordinates and of the displacement field is proposed; it is used to convert any boundary value problem for a linear elastic body into another one with different geometry, elastic moduli and boundary conditions. With this method, new problems, especially for inhomogeneous anisotropic bodies, may be solved by use of solutions of simpler ones. After a derivation of sufficient conditions to be fulfilled by such a transformation, the case of a linear homogeneous transformation is investigated in more detail. It is shown that a number of situations exist for which the transformed problem has a known analytical solution which can be used to derive the solution of the original problem straightforwardly. Special attention is paid to Saint-Venant-type anisotropy and to the derivation of the Green function for an infinite or a semi-infinite body. (10.1016/j.ijsolstr.2005.06.046)
  DOI : 10.1016/j.ijsolstr.2005.06.046
• Quasicontinuum Models of Dynamic Phase Transitions
  
  • Truskinovsky Lev
  • Vainchtein Anna
  Continuum Mechanics and Thermodynamics, Springer Verlag, 2006, 18 (1-2), pp.1-21. We propose a series of quasicontinuum approximations for the simplest lattice model of a fully dynamic martensitic phase transition in one dimension. The approximations are dispersive and include various non-classical corrections to both kinetic and potential energies. We show that the well-posed quasicontinuum theory can be constructed in such a way that the associated closed-form kinetic relation is in an excellent agreement with the predictions of the discrete theory. (10.1007/s00161-006-0018-5)
  DOI : 10.1007/s00161-006-0018-5
• TGV disc brake squeal
  
  • Lorang Xavier
  • Foy-Margiocchi Florence
  • Son Nguyen Quoc
  • Gautier Pierre-Etienne
  Journal of Sound and Vibration, Elsevier, 2006, 293, pp.735-746. The discomfort generated by the noise emission of braking systems in train has aroused recently many studies on the mechanical modeling of brake noise in France. A theoretical and numerical discussion on the phenomenon of brake squeal is given here in relation with some experimental data. This study is based upon a flutter instability analysis giving the unstable modes of the TGV brake system. (10.1016/j.jsv.2005.12.006)
  DOI : 10.1016/j.jsv.2005.12.006
• Experimental study and numerical simulation of non proportional loading paths using finite element crystal plasticity
  
  • Gérard Céline
  • Bacroix Brigitte
  • Bornert Michel
  • Brenner Renald
  • Cailletaud Georges
  • Castelnau Olivier
  • Crépin Jérôme
  • Forest Samuel
  • Leclercq Sylvain
  , 2006. This study aims at comparing numerical crystalline aggregates behaviour simulations performed by finite element, with experimental results of a study involving complex loading paths applied to a sheet of OFHC copper at room temperature. Material texture is taken into account. To investigate the plastic behaviour of materials during complex loading modes, combinations of sequences of simple loading paths such as tension, simple shear, rolling, cyclic tension-compression, with different orientations with regard to rolling direction, are considered. The material used in the study has been cold rolled and annealed. The so marked cubic texture is measured by X-ray diffraction. Specimen are mechanically and electrolytically polished, then marked with several gold microgrids, with a 4 $\mu m$ step, on a 500 $\mu m$ area, to measure local strain fields on the specimen surface. Furthermore, the global strain are measured by classical extensometry and strain-stress curves are plotted. Finite elements simulations corresponding to the experiment are realised with a polycrystalline aggregates taking into account the material microstructure. A 3D mesh which respects grain boundaries is used and the measured texture is represented. Several single crystal models are considered. They introduce the 12 slip systems of the octahedral families. Various assumptions are considered for the description of the self-hardening and of the latent hardening. The comparisons between the simulation and the experiments are made at two levels: the global level, with the description of the macroscopic stress-strain curve, and the local level, by considering the local fields. It is demonstrated that the whole batch of tests gives the user a very good information about the slip system interaction.
• On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: II-Application to cylindrical fibers
  
  • Lopez-Pamies Oscar
  • Ponte Castañeda Pedro
  Journal of the Mechanics and Physics of Solids, Elsevier, 2006, 54, pp.831-863. In Part I of this paper, we presented a general homogenization framework for determining the overall behavior, the evolution of the underlying microstructure, and the possible onset of macroscopic instabilities in fiber-reinforced elastomers subjected to finite deformations. In this work, we make use of this framework to generate specific results for general plane-strain loading of elastomers reinforced with aligned, cylindrical fibers. For the special case of rigid fibers and incompressible behavior for the matrix phase, closed-form, analytical results are obtained. The results suggest that the evolution of the microstructure has a dramatic effect on the effective response of the composite. Furthermore, in spite of the fact that both the matrix and the fibers are assumed to be strongly elliptic, the homogenized behavior is found to lose strong ellipticity at sufficiently large deformations, corresponding to the possible development of macroscopic instabilities [Geymonat, G., Müller, S., Triantafyllidis, N., 1993. Homogenization of nonlinearly elastic materials, macroscopic bifurcation and macroscopic loss of rank-one convexity. Arch. Rat. Mech. Anal. 122, 231–290]. The connection between the evolution of the microstructure and these macroscopic instabilities is put into evidence. In particular, when the reinforced elastomers are loaded in compression along the long, in-plane axis of the fibers, a certain type of “flopping” instability is detected, corresponding to the composite becoming infinitesimally soft to rotation of the fibers. (10.1016/j.jmps.2005.10.010)
  DOI : 10.1016/j.jmps.2005.10.010
• Elastomères sous chargement cyclique et durée de vie en fatigue
  
  • Raoult Ida
  • Stolz Claude
  , 2006.
• Analyse des solides déformables par la méthode des éléments finis
  
  • Bonnet Marc
  • Frangi A.
  , 2006, pp.320.
• Mesures de champs et identification de modèles de plasticité cristalline
  
  • Gérard Céline
  , 2006.
• Mechanical behaviour and temperature measurement during dynamic deformation on split Hopkinson bar of 304L stainless steel and 5754 aluminium alloy
  
  • Jovic C.
  • Wagner D.
  • Hervé P.
  • Gary Gérard
  • Lazarotto L.
  Journal de Physique IV Proceedings, EDP Sciences, 2006, 134, pp.1279-1285. The forming process of massive products at ambient temperature and at high speed of loading has not led to many scientific investigations up to now. Its understanding involves mechanical and thermal aspects that are strongly linked together (thermo-mechanical coupling). The adiabatic process generated at high strain rates, due to the short duration of the test that does not allow for thermal equilibrium, can induce thermal softening in the billet and modifications of the metallurgical microstructures. The tests are done with 304L stainless steel and 5754 aluminium alloy. A split Hopkinson bar is used for strain rates up to 2000 $^{{\rm s}-1}$. During the test, the temperature at specimen surface was measured with an infrared multi-detector (with a resolution area $43\,\mu$m $\times 43\,\mu$m and an frequency acquisition equal to 1 MHz). The measurement system allows for a temperature measurement along a line of the specimen surface. The focusing system is designed to eliminate the geometric and chromatic aberrations induced by the lenses and it allows for measurements at high strain rates with short specimens. With this system, it is shown that the temperature field is homogeneous along the sample during the complete duration of loading. Consequently, the Taylor-Quinney coefficient can be deduced from temperature measurements. (10.1051/jp4:2006134194)
  DOI : 10.1051/jp4:2006134194
• Macroscopic behavior and field fluctuations in viscoplastic composites: Second-order estimates versus full-field simulations
  
  • Idiart Martin
  • Moulinec Hervé
  • Ponte Castañeda Pedro
  • Suquet Pierre
  Journal of the Mechanics and Physics of Solids, Elsevier, 2006, 6, pp.201-208. This work presents a combined numerical and theoretical study of the effective behavior and statistics of the local fields in random viscoplastic composites. The full-field numerical simulations are based on the fast Fourier transform (FFT) algorithm [Moulinec, H., Suquet, P., 1994. A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. Paris II 318, 1417–1423], while the theoretical estimates follow from the so-called “second-order” procedure [Ponte Castañeda, P., 2002a. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory. J. Mech. Phys. Solids 50, 737–757]. Two-phase fiber composites with power-law phases are considered in detail, for two different heterogeneity contrasts corresponding to fiber-reinforced and fiber-weakened composites. Both the FFT simulations and the corresponding “second-order” estimates show that the strain-rate fluctuations in these systems increase significantly, becoming progressively more anisotropic, with increasing nonlinearity. In fact, the strain-rate fluctuations tend to become unbounded in the limiting case of ideally plastic composites. This phenomenon is shown to correspond to the localization of the strain field into bands running through the composite along certain preferred orientations determined by the loading conditions. The bands tend to avoid the fibers when they are stronger than the matrix, and to pass through the fibers when they are weaker than the matrix. In general, the “second-order” estimates are found to be in good agreement with the FFT simulations, even for high nonlinearities, and they improve, often in qualitative terms, on earlier nonlinear homogenization estimates. Thus, it is demonstrated that the “second-order” method can be used to extract accurate information not only for the macroscopic behavior, but also for the anisotropic distribution of the local fields in nonlinear composites. (10.1016/j.jmps.2005.11.004)
  DOI : 10.1016/j.jmps.2005.11.004
• A computational lifetime prediction of a thermal shock experiment. Part I: thermomechanical modelling and lifetime prediction
  
  • Amiable Sébastien
  • Chapuliot Stéphane
  • Constantinescu Andreï
  • Fissolo Antoine
  Fatigue and Fracture of Engineering Materials and Structures, Wiley-Blackwell, 2006, 29, pp.175-182. The SPLASH experiment has been designed in 1985 by the CEA to simulate thermal fatigue due to short cooling shocks on steel specimens and is similar to the device reported by Marsh in Ref. [1]. The purpose of this paper is to discuss the mechanical and the fatigue analysis of the experiment using results from FEM computations. The lifetime predictions are obtained using a modified dissipated energy with a maximal pressure term and agree with the experimental observations. The numerical analysis of the mechanical state shows an important evolution of the triaxiality ratio during the loading cycle. Further comparisons and discussions of the fatigue criteria are provided in the second part of the paper (Part II). (10.1111/j.1460-2695.2006.0976.x)
  DOI : 10.1111/j.1460-2695.2006.0976.x
• Topological sensitivity for 3D elastodynamic and acoustic inverse scattering in the time domain
  
  • Bonnet Marc
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2006, 195, pp.5239-5254. Building on previous work for 3D inverse scattering in the frequency domain, this article develops the concept of topological derivative for 3D elastic and acoustic-wave imaging of media of arbitrary geometry using data in the time domain. The topological derivative, which quantifies the sensitivity of the cost functional associated with the inverse scattering problem due to the creation at a specified location of an infinitesimal hole (for the elastodynamic case) or rigid inclusion (for the acoustic case), is found to be expressed in terms of the time convolution of the free field and a supplementary adjoint field. The derivation of the topological derivative follows the generic pattern proposed in previous studies, which is transposable to a variety of other physical problems. A numerical example, where the featured cost function is defined in terms of synthetic data arising from the scattering of plane acoustic waves by a rigid spherical inclusion, illustrates the utility of the topological derivative concept for defect identification using time-varying data. (10.1016/j.cma.2005.10.026)
  DOI : 10.1016/j.cma.2005.10.026
• FM-BEM and topological derivative applied to acoustic inverse scattering
  
  • Bonnet Marc
  • Nemitz Nicolas
  , 2006. This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally-small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving the free field and an adjoint field associated with the cost function. These fields are computed by means of a boundary element formulation accelerated by the Fast Multipole method. A computationally fast approach for performing a global preliminary search based on the available overspecified boundary data is thus defined. Its usefulness is demonstrated through results of numerical experiments on the qualitative identification of a hard obstacle in a bounded acoustic domain, for configurations featuring O(10⁵) nodal unknowns and O(10⁶) sampling points. (10.1007/978-3-540-47533-0_8)
  DOI : 10.1007/978-3-540-47533-0_8
• Nucleating-inclusion asymptotic for inverse problems in acoustics
  
  • Bonnet Marc
  • Guzina B. B.
  , 2006. No abstract provided
• Quasi-static and impact tests of Honeycomb
  
  • Gary Gérard
  • Klepaczko Janusz R
  Journal de Physique IV Proceedings, EDP Sciences, 2006, 134, pp.819-826. In this paper the quasi-static and instrumented compression impact testing of two kinds of aluminum-alloy honeycomb are reported. Those two types of honeycomb called Hard (H) and Soft (S) were tested. The specimens in cubical form of dimensions 60 mm $\times$ 60 mm $\times$ 120 mm were made with and without the front aluminum alloy plates (thickness 1.0 mm) cemented to the specimen two faces. The tests have been performed along the largest dimension that is 120 mm, which is parallel to the aluminum sheet profiles forming the honeycomb. A wide range of compression velocities from the quasi-static rate (V0 = 10 mm/min) to the highest impact velocity V6 = 120 m/s were applied. The total number of velocities applied, including the quasi-static loading, was six. Several series of tests were performed. The first two were carried out with the flat-ended strikers of specific masses, which were adequate to each impact velocity. In order to obtain an adequate displacement of crushing the condition of constant kinetic energy of a striker was assumed. In addition, conical strikers were applied with the cone angle 120$^{\circ}$. Application of the direct impact arrangement along with properly instrumented 9m long Hopkinson bar of Nylon with diameter 80 mm enabled for a wave dispersion analysis to be applied. The crushing force versus time could be exactly determined at the specimen-bar interface by application of an inverse technique along with the theory of visco-elastic wave propagation. (10.1051/jp4:2006134126)
  DOI : 10.1051/jp4:2006134126
• Mechanical properties of high density polyurethane foams: I. Effect of the density
  
  • Saint-Michel Fabrice
  • Chazeau Laurent
  • Cavaillé Jean-Yves
  • Chabert Emmanuelle
  Composites Science and Technology, Elsevier, 2006, 66, pp.2700-2708. This article presents the mechanical behaviour of rigid polyurethane foams with relative density (ρf/ρs) above 0,3. The parameter taken into account is the density, which controls the foam architecture. The mechanical properties of the foams, characterised by large deformation compression tests and dynamic mechanical analyses, were compared to two theoretical models: (i) the Gibson and Ashby approach, widely used for foam description and (ii) the 2 + 1 phase model from Christensen and Lo, generally used for the description of particulate composite materials. In the studied density range, it is shown that the second approach is more appropriate. Moreover, the stress–strain curve and in particular yield stress have been modelled using two different approaches by extension of this model to the non-linear domain. (10.1016/j.compscitech.2006.03.009)
  DOI : 10.1016/j.compscitech.2006.03.009
• Influence of the crack-tip hydride concentration on the fracture toughness of Zircaloy-4
  
  • Bertolino Graciela
  • Perez Ipiña J.
  • Meyer G.
  Journal of Nuclear Materials, Elsevier, 2006, 348, pp.205-212. The influence of a hydrogen concentration gradient at the crack-tip and hydride platelet orientation on the fracture toughness, fracture mode and micromechanisms of a Zircaloy-4 commercial alloy was studied. Fracture toughness was measured on CT specimens and the analysis was performed in terms of J-integral resistance curves at temperatures ranging from 293 to 473 K. Fracture toughness results of specimens containing higher hydrides concentration near the crack-tip region, preferentially orientated in the crack plane, were compared to those obtained from specimens with a homogeneous hydrogen distribution and different platelet orientation; specimens were obtained by charging them in loaded and unloaded condition, respectively. Changes on both macroscopic and microscopic fracture behaviour were observed at temperatures ranging from 293 to 343 K, and the results show the relevance of both hydride concentration and platelet orientation. The existence of a ductile-to-brittle transition is discussed at the light of these new results. (10.1016/j.jnucmat.2005.09.017)
  DOI : 10.1016/j.jnucmat.2005.09.017
• Microscopic and macroscopic instabilities in finitely strained porous elastomers
  
  • Michel J. C.
  • Lopez-Pamies O.
  • Ponte Castañeda P.
  • Triantafillydis N.
  Journal of the Mechanics and Physics of Solids, Elsevier, 2006, 55 (5), pp.900-938. The present work is an in-depth study of the connections between microstructural instabilities and their macroscopic manifestations-as captured through the effective properties-in finitely strained porous elastomers. The powerful second-order homogenization (SOH) technique initially developed for random media, is used for the first time here to study the onset of failure in periodic porous elastomers and the results are compared to more accurate finite element method (FEM) calculations. The influence of different microgeometries (random and periodic), initial porosity, matrix constitutive law and macroscopic load orientation on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition to the above-described stability-based onset-of-failure mechanisms, constraints on the principal solution are also addressed, thus giving a complete picture of the different possible failure mechanisms present in finitely strained porous elastomers. (10.1016/j.jmps.2006.11.006)
  DOI : 10.1016/j.jmps.2006.11.006
• New sulfonated pyrrole and pyrrole 3-carboxylic acid copolymer membranes via track-etched templates
  
  • Clochard M.-C
  • Baudin C
  • Betz N
  • Le Moël A
  • Bittencourt C
  • Houssiau L
  • Pireaux J.-J
  • Caldemaison Daniel
  Reactive and Functional Polymers, Elsevier, 2006, pp.1296. New copolymers of polypyrrole and poly(3-carboxylic acid pyrrole) have been synthesized via a diaphragmatic method using a track-etched polycarbonate matrix. The presence of carboxylic acid substituents enables the introduction of new functionalities such as sulfonate groups. The resulting copolymer membranes with tubules microstructure have been characterized through scanning electron microscopy, X-ray photoelectron spectroscopy, time-of-flight secondary ion mass spectrometry and FT-IR. By SEM, it was observed that ion-track trajectories can cross. XPS, ToF-SIMS and FT-IR spec-troscopy showed that it was possible to attach other molecules to the membrane. The polypyrrole copolymer membranes have exceptional thermal stabilities, with decomposition observed at 900 °C. (10.1016/j.reactfunctpolym.2006.03.012)
  DOI : 10.1016/j.reactfunctpolym.2006.03.012
• Inverse acoustic scattering by small-obstacle expansion of misfit function
  
  • Bonnet Marc
  , 2006. This article concerns an extension of the topological derivative concept for 3D inverse acoustic scattering problems, whereby the featured cost function J is expanded in powers of the characteristic size ϵ of a sound-hard scatterer about ϵ=0. The O(ϵ6) approximation of J is established for a small scatterer of arbitrary shape of given location embedded in an arbitrary acoustic domain, and generalized to several such scatterers. Simpler and more explicit versions of this result are obtained for a centrally-symmetric scatterer and a spherical scatterer. An approximate and computationally fast global search procedure is proposed, where the location and size of the unknown scatterer is estimated by minimizing the O(ϵ6) approximation of J over a search grid. Its usefulness is demonstrated on numerical experiments, where the identification of a spherical, ellipsoidal or banana-shaped scatterer embedded in a acoustic half-space from known acoustic pressure on the surface is considered. (10.1088/0266-5611/24/3/035022)
  DOI : 10.1088/0266-5611/24/3/035022
• An experimental study of square tube crushing under impact loading using a modified large scale SHPB
  
  • Zhao Han
  • Abdennadher Salim
  • Othman Ramzi
  International Journal of Impact Engineering, Elsevier, 2006, 32 (7), pp.1174-1189. This paper presents an experimental study on square tubes made from a rate insensitive material under static and impact loading. Rate insensitivity of the base material (Cu–Zn alloy) is confirmed by static and dynamic tests on small samples cut from the tubes. A direct impact large scale Hopkinson bar (80 mm diameter, 10 m length) system is used to perform tube crushing tests. A two-point measurement method is applied to extend measuring duration of the pressure bar, which is usually limited by its length. The proposed method permits to monitor the whole tube crushing process. Static and impact tests (7–15 m/s) on these square tubes reveal that there is a significant increase under impact loading of both initial and successive peak loads with respect to quasi-static loading. Such a study is useful for the understanding of strength enhancement under impact loading observed for cellular materials such as honeycombs. (10.1016/j.ijimpeng.2004.09.013)
  DOI : 10.1016/j.ijimpeng.2004.09.013
• Analyse modale sans Transformée de Fourier
  
  • Lozada José
  • Boutillon Xavier
  • David Bertrand
  , 2006, pp.4 p.. L'analyse modale traditionnelle fait appel à la transformée de Fourier pour l'estimation de la fréquence modale (et éventuellement de l'amortissement modal) et utilise le rapport spectral entre réponse vibratoire et force excitatrice pour estimer les amplitudes (et éventuellement les phases) modales. Cette technique est peu performante pour estimer des modes dont les fréquences sont proches en regard de leur amortissement intrinsèque. Nous gardons le mode opératoire traditionnel de l'excitation par marteau d'impact et capture de la réponse vibratoire par accéléromètre. Nous estimons tout d'abord le filtre $g$ à appliquer à chaque excitation $f(t)$ du système pour la transformer en impulsion: $f{\ast}g={\delta}$. L'application de ce même filtre à la réponse vibratoire donne ainsi la réponse impulsionnelle normée en chaque point. En théorie modale linéaire, cette réponse impulsionnelle prend la forme d'une somme de sinusoïdes exponentiellement décroissantes. Nous pouvons donc leur appliquer une analyse spectrale paramétrique (ici, l'algorithme ESPRIT) qui permet d'obtenir les paramètres modaux (fréquence, amortissement, amplitude et phase éventuellement) avec une précision bien meilleure que celle offerte par l'analyse de Fourier. Nous présenterons en particulier l'application de cette méthode à la séparation entre le mouvement transitoire de corps rigide et les premiers modes de vibration d'une touche de piano.