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Coupling resonance mechanism of interfacial fatigue stratification of adhesive and/or welding butt joint symmetric and/or antisymmetric structures excited by horizontal shear waves are investigated by forced propagation analytical solutions derived by plane wave perturbation methods, integral transformation methods and global matrix methods. The influence of materials on the coupled resonance frequency is analyzed and discussed by the analytical methods. Coupling resonance of interface shear stress is a structure inherent property. Even a very small excitation amplitude at the coupling resonance frequency can result in interface shear delamination. The coupling resonance frequency decreases with the increase of interlayer thickness or shear wave velocity difference between substrate and interlayer. The results could be applied to layered and/or anti-layered structural design.

An overview of recent work on the interaction of elastic waves with dislocations is given. The perspective is provided by the wish to develop nonintrusive tools to probe plastic behavior in materials. For simplicity, ideas and methods are first worked out in two dimensions, and the results in three dimensions are then described. These results explain a number of recent, hitherto unexplained, experimental findings. The latter include the frequency dependence of ultrasound attenuation in copper, the visualization of the scattering of surface elastic waves by isolated dislocations in LiNbO₃, and the ratio of longitudinal to transverse wave attenuation in a number of materials.

Specific results reviewed include the scattering amplitude for the scattering of an elastic wave by a screw, as well as an edge, dislocation in two dimensions, the scattering amplitudes for an elastic wave by a pinned dislocation segment in an infinite elastic medium, and the wave scattering by a sub-surface dislocation in a semi-infinite medium. Also, using a multiple scattering formalism, expressions are given for the attenuation coefficient and the effective speed for coherent wave propagation in the cases of anti-plane waves propagating in a medium filled with many, randomly placed screw dislocations; in-plane waves in a medium similarly filled with randomly placed edge dislocations with randomly oriented Burgers vectors; elastic waves in a three-dimensional medium filled with randomly placed and oriented dislocation line segments, also with randomly oriented Burgers vectors; and elastic waves in a model three-dimensional polycrystal, with only low angle grain boundaries modeled as arrays of dislocation line segments.

The reflection and transmission of a time-harmonic plane wave in an isotropic elastic medium by a three-dimensional diffraction grating is investigated. If the diffractive structure involves an impenetrable surface, we study the first, second, third and fourth kind boundary value problems for the Navier equation in an unbounded domain by the variational approach. A radiation condition based on the Rayleigh expansion of the quasi-periodic solutions is presented. Existence of solutions in Sobolev spaces is established if the grating profile is a two-dimensional Lipschitz surface, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. Similar solvability results are obtained for multilayered transmission gratings in the case of an incident pressure wave. Moreover, by a periodic Rellich identity, uniqueness of the solution to the first kind (Dirichlet) boundary value problem is established for all frequencies under the assumption that the impenetrable surface is given by the graph of a Lipschitz function.

Propagation of elastic waves is studied in a 1D medium containing two cracks. The latter are modeled by smooth nonlinear jump conditions accounting for the finite, non-null compressibility of real cracks. The evolution equations are written in the form of a system of two nonlinear neutral delay differential equations, leading to a well-posed Cauchy problem. Perturbation analysis indicates that, under periodic excitation, the periodic solutions oscillate around positive mean values, which increase with the forcing level. This typically nonlinear phenomenon offers non-destructive means to evaluate the cracks. Existence, uniqueness and attractivity of periodic solutions is then examined. At some particular values of the ratio between the wave travel time and the period of the source, results are obtained whatever the forcing level. With a much larger set of ratios but at small forcing levels, results are obtained under a Diophantine condition. Lastly, numerical experiments are proposed to illustrate the behavior of the periodic diffracted waves.

This work deals with the extension of the partition of unity finite element method (PUFEM) "(Comput. Meth. Appl. Mech. Eng.139 (1996) pp. 289–314; Int. J. Numer. Math. Eng.40 (1997) 727–758)" to solve wave problems involving propagation, transmission and reflection in layered elastic media. The proposed method consists of applying the plane wave basis decomposition to the elastic wave equation in each layer of the elastic medium and then enforce necessary continuity conditions at the interfaces through the use of Lagrange multipliers. The accuracy and effectiveness of the proposed technique is determined by comparing results for selected problems with known analytical solutions. Complementary results dealing with the modeling of pure Rayleigh waves are also presented where the PUFEM model incorporates information about the pressure and shear waves rather than the Rayleigh wave itself.

A new high-order local Absorbing Boundary Condition (ABC) has been recently proposed for use on an artificial boundary for time-dependent elastic waves in unbounded domains, in two dimensions. It is based on the stress–velocity formulation of the elastodynamics problem, and on the general Complete Radiation Boundary Condition (CRBC) approach, originally devised by Hagstrom and Warburton in 2009. The work presented here is a sequel to previous work that concentrated on the stability of the scheme; this is the first known high-order ABC for elastodynamics which is long-time stable. Stability was established both theoretically and numerically. The present paper focuses on the accuracy of the scheme. In particular, two accuracy-related issues are investigated. First, the reflection coefficients associated with the new CRBC for different types of incident and reflected elastic waves are analyzed. Second, various choices of computational parameters for the CRBC, and their effect on the accuracy, are discussed. These choices include the optimal coefficients proposed by Hagstrom and Warburton for the acoustic case, and a simplified formula for these coefficients. A finite difference discretization is employed in space and time. Numerical examples are used to experiment with the scheme and demonstrate the above-mentioned accuracy issues.

In this review paper, the use of the Time Reversal (TR) method as a computational tool for solving some classes of inverse problems is surveyed. The basics of computational TR are explained, using the scalar wave equation as a simple model. The application of TR to various problems in acoustics and elastodynamics is reviewed, in a selective and biased way as it leans on the author's personal view, referring to representative articles published on the subject.

Time reversal is a powerful procedure in application fields involving wave propagation. It is based on the invariance of the wave equations, in the absence of dissipation, in the time direction. This allows going backward in time to recover past events. We use time reversal to recover the location of a source applied at the initial time based on measurements at a later time. We generalize the procedure previously developed for the scalar wave equation¹ to elastodynamics. We show that the technique is quite robust, sometimes even in the presence of very high noise levels. Also it is not very sensitive to the medium characterizations, when a sufficient amount of measurement data is available. We extend previous work to get good refocusing for multiple sources. We introduce a new score to assess the quality of the numerical solution for the refocusing problem which produces good results. Furthermore, we use the refocusing technique as a basis for scatterer location recovery. By adding noise in a controlled manner we improve the scheme of finding the location of the scatterer.

We investigate the dynamical properties of two isolated steps on the surface. We present the solution of the full dynamical problem arising from the absence of translation symmetry in two dimensions due to extended surface steps on the surface boundary of an insulating substrate. The calculations concern in particular the dynamics of localized modes of an atomic step on the surface of a cubic lattice. The theoretical approach determines the vibrational field in both steps. The matching method, which constitutes a powerful formalism for determining the vibrational properties of such disordered surfaces, is used. The model presented in this study consists of two monatomic steps as the interface between three coupled semi-infinite and single semi-infinite atomic layers. The dynamical properties of the perfect waveguides are presented and calculated numerically. The breakdown of translational symmetry perpendicular to the step edges gives rise to several Raleigh-like branches localized in the neighborhood of the steps. Typical dispersion curves for these modes along the steps are given with their polarization.

The effect on the vibrational properties of nanostructures at the interface between two thin films is presented. The model used consists of the coupling of two semi-infinite plans A and B having three and two atomic layers, respectively. Theoretical calculations of localized phonon modes and vibrational field were carried out using the matching procedure. Close to the interface, the transversal translational symmetry is broken down inducing Raleigh-like branches. The polarization degeneracy of the ordered surface Raleigh mode in the longitudinal direction is lifted. The presence of acoustic and optical-like phonons is discussed in terms of the elastic constant forces. The density of states and the spectral densities are presented for sample atomic sites. A hyperfine resonance structure is obtained. It allows the analysis of the dynamical evolution from thin film A to thin film B.

We have theoretically resolved phonon excitations in quasi-two-dimensional organic crystals of polyacenic semiconductor material which may be obtained by the pyrolytic treatment of phenol-formaldehyde resin. A model for studying the dynamical properties using three polyacene chains is proposed with the aim to present the vibrational properties of this structure. It employs the formalism of solid states in two dimensions which admit phonons. A simulation process of the two-dimensional lattice structure shows that elastic waves may explain the existence of vibrational modes in the frequency range 100–400 cm^-1. The presence of acoustic and optical like phonons is discussed in terms of the elastic force constants. A hyperfine resonance structure is obtained. It allows the analysis of the dynamical evolution in thin films of polyacene. It is found that the behavior of the phonon density of states exhibits resonance between modes in the structure.

The dynamic response of the seabed to ocean surface waves is treated analytically on the basis of an elastic wave theory in a soil-water mixture. The seabed is modeled as the aggregate of a poro-elastic soil-skeleton with air-containing pore-water, from which a general solution is presented for a homogeneous bed of infinite thickness. Two kinds of compressive waves and one shear wave are shown to exist in the seabed and their phases and attenuation characteristics are clarified. Based on the propagation of these elastic waves, exact solutions for the dynamic response in pore-water pressure and displacements of porous soil-skeleton are derived in physically lucid form. It is found that the relative motion between the soil and water is produced by the second compressive wave, but not from other elastic waves. The present solution is shown to include the well-known quasi-static solution given by Yamamoto et al. (1978), as a limiting case. By comparing the present dynamic solution with that of quasi-static state, two important nondimensional parameters are presented to discuss the applicability of each solution.

The scattering of plane elastic waves by an anisotropic layered medium in the case of the six-beam diffraction is considered. The matrix method for solving wave equations is developed. The conversion coefficients $C_{ij}$ for the three types of incident waves (horizontally polarized shear wave, vertically polarized shear wave and longitudinal wave) are defined. Representations of coefficients $C_{ij}$ through elements of transfer matrix are found. The method for coefficients $C_{ij}$ calculations is presented. It does not require the solving of algebraic problem on eigenvalues for waves in an anisotropic layer. Some features of the functional dependencies of $C_{ij}$ on the angles of incidence, wave frequency and layer thickness are demonstrated on several examples of the crystals in a three-layer model. It is shown that the conversions SH wave into SV waves and SV wave into SH waves are equivalent.

The propagational characteristics of free waves in wave guides can be utilized for NDE, vibration reduction, and oil exploration. A vast of researches have been conducted on isotropic and anisotropic laminated plates, but few concerning the behavior in high frequency range or at large wave numbers, for which numerical instability may generally be encountered in conventional analysis methods. Based on the state equation for anisotropic elasticity, this paper constructs the formulations for the method of reverberation-ray matrix to analyze the wave propagation in anisotropic elastic laminated plates. Since unknown wave amplitudes are appropriately retained in the formulations, large numbers at high frequencies are excluded, making the calculation stable in the high frequency range. The matrix inverse operation is also avoided in the scattering relations to assure the stability in the low frequency range. Numerical examples are presented and good agreement is obtained.

We consider the (linear) elastic wave equation and construct asymptotic expansions of waves reflected by boundaries in various situations. We treat the case where a discontinuous wave like the delta function hits the boundary and the total reflection happens. We also deal with the case where a wave is reflected by a hole empty or full of some liquid, and examine the reflection rate of the backward reflected wave.