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Exact analytical treatment of the interaction of harmonic elastic waves with n-layered anisotropic plates is presented. Each layer of the plate can possess up to as low as monoclinic symmetry and thus allowing results for higher symmetry materials such as orthotropic, transversely isotropic, cubic, and isotropic to be obtained as special cases. The wave is allowed to propagate along an arbitrary angle from the normal to the plate as well as along any azimuthal angle. Solutions are obtained by using the transfer matrix method. According to this method formal solutions for each layer are derived and expressed in terms of wave amplitudes. By eliminating these amplitudes the stresses and displacements on one side of the layer are related to those of the other side. By satisfying appropriate continuity conditions at interlayer interfaces a global transfer matrix can be constructed which relates the displacements and stresses on one side of the plate to those on the other. Invoking appropriate boundary conditions on the plates outer boundaries a large variety of important problems can be solved. Of these mention is made of the propagation of free waves on the plate and the propagation of waves in a periodic media consisting of a periodic repetition of the plate. Confidence is the approach and results are confirmed by comparisons with whatever is available from specialized solutions. A variety of numerical illustrations are included.

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Reflection and transmission of compressional waves by a stratification with discontinuities in density and/or sound speedConcepts from the theory of interacting continua are employed to develop constitutive relations for liquid and/or gas saturated elastic porous media. The model is formulated by defining intrinsic stress tensors and densities in terms of the partial stress tensors, partial densities, and actual volume fractions occupied by each component. It is assumed that the constitutive law for each component as a single continuum relates intrinsic pressure to intrinsic deformation. Relative motion between the constituents is allowed through simple Darcy-type expressions. The governing equations together with the constitutive relations are used to investigate the propagation of both harmonic and transient pulses. In general three modes of wave propagation exist. In the case of a transient pulse, these modes lead to a three-wave structure. Laplace transform techniques are used to derive closed-form solutions for transient loading for two limiting values of viscous coupling (Le., weak viscous coupling, strong viscous coupling). Strong viscous coupling results in the coalescence of the three wave fronts into a single front. Solutions for the genera] case of transient loading are obtained by numerical inversion of the Laplace transforms.

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