Radiation mode model for multilayered structures

摘要

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 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 research. 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. 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 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.