PERIODIC NONSMOOTH COORDINATES FOR MODELING ACOUSTIC WAVES IN LAYERED ELASTIC MEDIA

摘要

Analytical tool for modeling elastic waves in periodic composite materials with micro inclusions is introduced. The method effectively eliminates discontinuities from the material physical characteristics in such a way that the resultant equations can be analyzed within the class of smooth systems without matching different pieces of solutions. The idea is based on introduction of two different types of spatial coordinates, one of which associates with the wave length while another one is dictated by the microstructural geometry of the material. In contrast to conventional two variables or multiple scale expansions, the fast microstructural coordinate is chosen to be non-smooth and periodic in order to adequately fit physical properties of the material. As a result, closed form asymptotic solutions combining macro- and micro-scale wave effects are obtained. Such solutions visualize both global and local details of acoustic waves, for instance, the possibility of beat-wise mode shapes and effective directional anisotropy. The subharmonic spatial beats occur when wave lengths are close to the period of material.