In the present study viscoelasticity is introduced in the mode model and the orthogonality condition is adapted for viscous media. The expansion of convergent acoustic Gaussian beams in terms of radiation modes for viscoelastic media is studied as well. The effects on the reflected and transmitted profiles of acoustic beams incident from an ideal liquid onto a viscoelastic plate are shown and physically explained. It is shown that focusing the incident beam can suppress divergence effects and gives the possibility to measure shear wave attenuation coefficients.

The scattering of a Gaussian beam by a rectangular crack is studied by means of the radiation mode model. The orthogonal set of modes for a L/S/V structure is derived, and a general mode decomposition formula is developed. The influence of a crack on the reflected and transmitted fields of a bounded beam, incident at critical angles of the L/S/L- and the L/S/V structure, is studied and physical interpretations are given. From those interpretations, the starting point of the crack is deduced along with the length and distance to the surface. Effects on focused beams are considered as well.

Interaction of bounded acoustic beams with multilayered structures has been investigated extensively by several researchers in the last half of this century. It was W. T. Thompson 9 who treated the problem the first time and introduced the "transfer matrix". This matrix describes the relation between the displacements and stresses at the top of a layer and those at the bottom of the layer. It was the initial impetus for further In this paper, a multilayered solid embedded in a liquid is considered. The aim of this paper is to present the modelling of the interaction of bounded acoustic beams with a multilayer by means of the Mode Method 1,2,3,4,5 .The study of the reflected profile of an incident Gaussian beam enables us to characterize material parameters or to estimate the elastic properties of the reflector. It is known 8,13 that computational difficulties occur for high frequencies, thick layers and large angles of incidence. We dealt with this problem in our model by restricting the spectrum of radiation modes to the most substantial ones.In the first section, the general decomposition formula in radiation modes for a multilayered structure is derived. In the second section, an illustrative application is given. Determination of the residual stress in a plastically deformed plate is developed. In a first subsection, the modelling of the plastically deformed plate is worked out. A parabolic distributed residual stress is chosen in subsection two. In the final subsection, computations are done. It is shown that the residual stress can be measured by means of the reflected amplitude and phase profile of a Gaussian beam incident at a Lamb angle. research. 6-8-10-13 1. Construction of the orthogonal set of radiation modes for a multilayered structure.Consider a multilayered structure of total thickness d embedded in an elastic liquid. We assume n viscoelastic solid layers with infinite extent in the z-direction. Layer j has thickness dj and lower interface at y j _ 1 and upper interface at y j , see fig. 1.

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