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The propagation of surface (Rayleigh) waves over a rotating orthorhombic crystal is studied. The crystal possesses three crystallographic axes, normal to the symmetry planes: the half¿space is cut along a plane normal to one of these axes, the wave travels in the direction of another, and the rotation occurs at a uniform rate about any of the three axes. The secular equation for the surface wave speed is found explicitly; in contrast to the non¿rotating case, it is dispersive (frequency dependent). Both Coriolis and centrifugal accelerations appear in the equations of motion: none can be neglected in favour of the other, even at small rotation rates. peer-reviewed

International audience; Etude des pots acoustiques dans les églises médiévales et modernes avec l'exposition de questionnements, leur nature et l'entendue de ceux-ci, proposition de grilles d'analyse et sensibilisation à la communauté acoustique pour sauver ce patrimoine.

Attention is given to surface waves of shear-horizontal modes in piezoelectric crystals permitting the decoupling between an elastic in-plane Rayleigh wave and a piezoacoustic anti-plane Bleustein-Gulyaev wave. Specifically, the crystals possess $\bar{4}$ symmetry (inclusive of $\bar{4}2$m, $\bar{4}3$m, and 23 classes) and the boundary is any plane containing the normal to a symmetry plane (rotated $Y$-cuts about the $Z$ axis). The secular equation is obtained explicitly as a polynomial not only for the metallized boundary condition but, in contrast to previous studies on the subject, also for other types of boundary conditions. For the metallized surface problem, the secular equation is a quadratic in the squared wave speed; for the un-metallized surface problem, it is a sextic in the squared wave speed; for the thin conducting boundary problem, it is of degree 16 in the speed. The relevant root of the secular equation can be identified and the complete solution is then found (attenuation factors, field profiles, etc.). The influences of the cut angle and of the conductance of the adjoining medium are illustrated numerically for GaAs ($\bar{4}3$m), BaLaGa$_3$O$_7$ ($\bar{4}2$m) and Bi$_{12}$GeO$_{20}$ (23). Indications are given on how to apply the method to crystals with 222 symmetry.

15 pages

Two semi-infinite bodies made of prestressed, homogeneous, Bell-constrained, hyperelastic materials are perfectly bonded along a plane interface. The half-space have been subjected to finite pure homogeneous predeformations, with distinct stretch ratios but common principal axes, and such that the interface is a common principal plane of strain. Constant loads are applied at infinity to maintain the deformations and the influence of these loads on the propagation of small-amplitude interface (Stoneley) waves is examined. In particular, the secular equation is found and necessary and sufficient conditions to be satisfied by the stretch ratios to ensure the existence of such waves are given. As the loads vary, the Stoneley wave speed varies accordingly: the upper bound is the “limiting speed” (given explicitly), beyond which the wave amplitude cannot decay away from the interface; the lower bound is zero, where the interface might become unstable. The treatment parallels the one followed for the incompressible case and the differences due to the Bell constraint are highlighted. Finally, the analysis is specialized to specific strain energy densities and to the case where the bimaterial is uniformly deforemd (that is when the stretch ratios for the upper half-space are equal to those for the lower half-space.) Numerical results are given for “simple hyperelastic Bell” materials and for “Bells” empirical model” materials, and compared to the results for neo-Hookean incompressible materials.

12 pages

Journal article Some relationships, fundamental to the resolution of interface wave problems, are presented. These equations allow for the derivation of explicit secular equations for problems involving waves localized near the plane boundary of anisotropic elastic half-spaces, such as Rayleigh, Scholte, or Stoneley waves. They are obtained rapidly, without recourse to the Stroh formalism. As an application, the problems of Stoneley wave propagation and of interface stability for misaligned predeformed incompressible halfspaces are treated. The upper and lower half-spaces are made of the same material, subject to the same prestress, and are rigidly bonded along a common principal plane. The principal axes in this plane do not, however, coincide, and the wave propagation is studied in the direction of the bisectrix of the angle between a principal axis of the upper half-space and a principal axis of the lower half-space. peer-reviewed

An isotropic elastic half-space is prestrained so that two of the principal axes of strain lie in the bounding plane, which itself remains free of traction. The material is subject to an isotropic constraint of arbitrary nature. A surface wave is propagated sinusoidally along the bounding surface in the direction of a principal axis of strain and decays away from the surface. The exact secular equation is derived by a direct method for such a principal surface wave; it is cubic in a quantity whose square is linearly related to the squared wave speed. For the prestrained material, replacing the squared wave speed by zero gives an explicit bifurcation, or stability, criterion. Conditions on the existence and uniqueness of surface waves are given. The bifurcation criterion is derived for specific strain energies in the case of four isotropic constraints: those of incompressibility, Bell, constant area, and Ericksen. In each case investigated, the bifurcation criterion is found to be of a universal nature in that it depends only on the principal stretches, not on the material constants. Some results related to the surface stability of arterial wall mechanics are also presented.

New exact solutions are exhibited within the framework of finite viscoelasticity. More precisely, the solutions correspond to finite-amplitude, transverse, linearly polarized, inhomogeneous motions superposed upon a finite homogeneous static deformation. The viscoelastic body is composed of a Mooney–Rivlin viscoelastic solid, whose constitutive equation consists in the sum of an elastic part (Mooney–Rivlin hyperelastic model) and a viscous part (Newtonian viscous fluid model). The analysis shows that the results are similar to those obtained for the purely elastic case; inter alia, the normals to the planes of constant phase and to the planes of constant amplitude must be orthogonal and conjugate with respect to the B-ellipsoid, where B is the left Cauchy–Green strain tensor associated with the initial large static deformation. However, when the constitutive equation is specialized either to the case of a neo-Hookean viscoelastic solid or to the case of a Newtonian viscous fluid, a greater variety of solutions arises, with no counterpart in the purely elastic case. These solutions include travelling inhomogeneous finite-amplitude damped waves and standing damped waves. © 2004 Elsevier B.V. All rights reserved.

The stability of a Bell-constrained half-space in compression is studied. To this end, the propagation of Rayleigh waves on the surface of the material when it is maintained in a static state of triaxial prestrain is considered. The prestrain is such that the free surface of the half-space is a principal plane of deformation. The exact secular equation is established for surface waves travelling in a principal direction of strain with attenuation along the principal direction normal to the free plane. As the half-space is put under increasing compressive loads, the speed of the wave eventually tends to zero and the bifurcation criterion, or stability equation, is reached. Then the analysis is specialized to specific forms of strain-energy functions and prestrain, and comparisons are made with results previously obtained in the case of incompressible neo-Hookean or Mooney-Rivlin materials. It is found that these rubber-like incompressible materials may be compressed more than "Bell empirical model" materials, but not as much as "Bell simple hyperelastic" materials, before the critical stretches, solutions to the bifurcation criterion, are reached. In passing, some classes of incompressible materials which possess a relative universal bifurcation criterion are presented. peer-reviewed

A new type of interface acoustic waves (IAW) is presented, for single-crystal orthotropic twins bonded symmetrically along a plane containing only one common crystallographic axis. The effective boundary conditions show that the waves are linearly polarized at the interface, either transversally or longitudinally. Then the secular equation is obtained in full analytical form using new relationships for the displacement-traction quadrivector at the interface. For gallium arsenide and for silicon, it is found that the IAWs with transverse (resp. longitudinal) polarization at the interface are of the Stoneley (resp. leaky) type. peer-reviewed

Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain. The surface wave propagates in a principal direction of strain and is attenuated in another principal direction, orthogonal to the free surface. For these waves, the secular equation giving the speed of propagation is established by the method of first integrals. This equation is not the same as the secular equation for incompressible half-spaces, even though the Bell constraint and the incompressibility constraint coincide in the isotropic infinitesimal limit. peer-reviewed

International audience

The existence of a two-partial Rayleigh wave coupled to an electrical field in 2 mm piezoelectric crystals is known but has rarely been investigated analytically. It turns out that the Z cut X propagation problem can be fully solved, up to the derivation of the secular equation as a polynomial in the squared wave speed. For the metallized (unmetallized) boundary condition, the polynomial is of degree 10 (48). The relevant root is readily identified and the full description of the mechanical and electrical fields follows. The results are illustrated in the case of the superstrong piezoelectric crystal, potassium niobate, for which the effective piezoelectric coupling coefficient is calculated to be about 0.1. peer-reviewed

Developing new high resolution focusing and imaging techniques for audible vibrational and acoustic sources is an important problem to solve in acoustics. Methods of this kind are notably useful to locally excite and analyse complex vibroacoustic structures with high resolution capabilities, which is particularly important when the size of the studied objects is smaller than the wavelength. The desired technique should be fast, accurate, flexible, and non-invasive. This technique must be used to study both vibrational and acoustic sources. This work shows the development of such a technique, based on the time reversal sink, which has been sofar only implemented for ultrasonic and electromagnetic waves focusing (not for imaging). The time reversal sink method is extended to hyper-resolution focusing for low frequency acoustic sources. This method provides a way to excite locally a structure with high intensity and high resolution capabilities, even at low frequency. However, we show that this method is difficult to implement in real world cases becauses it is an invasive focusing technique. Nevertheless, we present in this manuscript a new imaging technique of vibrational and acoustic sources, based on the time reversal sink. This is a new non-invasive technique, with high resolution capabilities. This technique uses the same array measurement techniques than beamforming and near-field acoustic holography, and provides an elegant and powerful way to obtain high resolution images of vibrational and acoustic sources at low frequency. This new method is extensively described and analysed, and applied to impact sources on a clamped plate, acoustic sources in a free field configuration and underwater acoustic sources in a deep water channel. This method has also been applied to the imaging of acoustic sources on a classical guitar. The results presented show high resolution, fast and reliable capabilities of this new powerfull imaging technique, that shows similar capabilities than those of nearfield acoustic holography and better results than those of beamforming and time reversal backpropagation at low frequency.; Le développement de techniques de focalisation et d'imagerie à haute résolution pour les sources acoustiques et vibratoires à basse fréquence est l'un des enjeux de la recherche actuelle en acoustique, notamment pour exciter localement et analyser des structures vibroacoustiques complexes tout en conservant des propriétés de haute résolution. Ces propriétés sont nécessaires lorsque la taille des objets étudiés est plus petite que la longueur d'onde mise en jeu. Nous désirons une méthode flexible, rapide, précise, non invasive, et unifiée d'excitation et d'analyse. Celle-ci doit être applicable tant dans le domaine des vibrations dans les structures que dans le domaine des ondes acoustiques tridimensionnelles. Pour cela, nous nous basons sur la technique du puits à retournement temporel, qui n'a, à ce jour, été mise en oeuvre que pour la focalisation d'ondes de Lamb dans une cavité ergodique ou avec des ondes électromagnétiques. Aucune technique d'imagerie n'a, avant cette thèse, été dérivée du puits à retournement temporel. La méthode du puits à retournement temporel est adaptée pour la focalisation à basse fréquence. Elle permet d'exciter localement une structure avec une grande intensité, et possède des capacités de super-résolution. Malgré tout, nous démontrons que cette méthode est difficilement applicable en situation pratique, puisqu'elle fait perdre le caractère non invasif nécessaire à la plupart des applications. En revanche, nous présentons dans ce manuscrit une technique nouvelle d'imagerie de sources vibratoires et acoustiques, basée sur le puits à retournement temporel. Cette technique non invasive d'imagerie, utilisant des dispositifs de mesure similaires aux techniques de formations de voies ou d'holographie en champ proche, permet d'obtenir une image des sources vibratoires ou acoustiques à très haute résolution de manière rapide. L'approche de cette nouvelle méthode d'imagerie est décrite. Des applications à l'imagerie de sources d'impact sur une plaque encastrée, ainsi qu'à l'imagerie de sources acoustiques en champ libre et en milieu sous-marin profond sont proposées. Une application à l'imagerie de sources acoustiques à basse fréquence sur une guitare est développée. Ces résultats représentent les premières applications de l'imagerie par puits à retournement temporel numérique. Les limites, la théorie, et la mise en oeuvre de cette technique d'imagerie à haute résolution sont étudiées et détaillées. Il est démontré que cet outil possède des performances et des limites similaires à l'holographie en champ proche, tout en dépassant les capacités à basse fréquence des techniques classiques de localisation limitées en résolution couramment utilisées, comme le beamforming ou le retournement temporel.