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Surface wave excitation and propagation in a half space with a continuous dependence of elastic properties on depth has been considered. The total wave field generated by a given surface load can be repre sented as a convolution of the Green's matrix of the medium with the vector of surface stresses, while the trav eling surface waves are described by the residues from the poles of the Green's matrix Fourier symbol. Com parison of the gradient and multilayer models shows that with a high enough number of partitions (layers), the dispersion properties and amplitude-frequency characteristics of surface waves in FGMs are described by the curves obtained upon a steplike approximation of gradient properties; however, with high contrast properties, the multilayer model can be more time consuming. The effect of the vertical inhomogeneity of the medium on the surface wave characteristics has been analyzed for a series of typical dependences occur ring in micro and nanocoatings due to diffusions or technological features of sputtering and gluing of pro tective films.

Propagation of time-harmonic plane elastic waves in infinite elastic composite materials consisting of linear elastic matrix and rigid penny-shaped inclusions is investigated in this paper. The inclusions are allowed to translate and rotate in the matrix. First, the three-dimensional (3-D) wave scattering problem by a single inclusion is reduced to a system of boundary integral equations for the stress jumps across the inclusion-surfaces. A boundary element method (BEM) is developed for solving the boundary integral equations numerically. Far-field scattering amplitudes and complex wave numbers are computed by using the stress jumps. Then the solution of the single scattering problem is applied to estimate the effective dynamic parameters of the composite materials containing randomly distributed inclusions of dilute concentration. Numerical results for the attenuation coefficient and the effective velocity of longitudinal and transverse waves in infinite elastic composites containing parallel and randomly oriented rigid penny-shaped inclusions of equal size and equal mass are presented and discussed. The effects of the wave frequency, the inclusion mass, the inclusion density and the inclusion orientation or the direction of the wave incidence on the attenuation coefficient and the effective wave velocities are analyzed. The results presented in this paper are compared with the available analytical results in the low-frequency range.

A B S T R A C T In this paper, transient thermoelastic crack analysis in two-dimensional, isotropic, continuously non-homogeneous and linear elastic functionally graded materials subjected to a thermal shock is presented. The Laplace transform technique is used to eliminate the time dependence of the governing equations of the linear coupled thermoelasticity. Fundamental solutions for isotropic, homogeneous and linear elastic solids in the Laplacetransformed domain are applied to derive boundary-domain integral equations for the mechanical and thermal fields. The radial integration method is employed to transform the domain integrals into the boundary integrals. A collocation-based boundary element method is implemented for the spatial discretization of the boundary-domain integral equations. The time-dependent numerical solutions are obtained by using Stehfest's inversion algorithm. Numerical results are presented and discussed to show the influences of the material gradation, the thermo-mechanical coupling, the crack orientation and the thermal shock loading on the dynamic stress intensity factors.Keywords boundary element method; dynamic stress intensity factors; functionally graded materials; Laplace transform; radial integration method; thermal shock. N O M E N C L A T U R Ea = half crack length a j i = unknown expansion coefficients b j = unknown expansion coefficients c (x) = specific heat at constant strain c 0 (x) = free-term coefficient c 0 jk (x) = free-term coefficients c i jkl (x) = elasticity tensor d A = support size for the application point A E(x) = Young's modulus h = semi-height of the FG plate H(t) = Heaviside step function I = identity matrix k(x) = thermal conductivitȳ K ± I (t) = normalized mode-I dynamic stress intensity factor at the crack-tips x 1 = ±ā K ± I I (t) = normalized mode-II dynamic stress intensity factor at the crack-tips x 1 = ±a N = total number of the unknown quantities N A = total number of the application points N s = total number of the approximation terms N q = total number of the boundary elements N d = total number of the internal points N w = total number of the boundary nodes N a (ξ ) = standard shape functions for quadratic elements n i = components of the outward unit normal vector Correspondence: A. Ekhlakov,

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