Transient wave propagation normal to the layering of a finite layered medium

Abstract

Plane wave propagation in the direction normal to the layering of a periodically layered medium is studied. A period consists of two layers of homogeneous, isotropic, linear elastic or viscoelastic materials. The layered medium is of finite extent and hence consists of a finite number of layers. A theory is presented by which the layered medium is replaced by an “equivalent” linear homogeneous viscoelastic material such that the stress or the velocity in the latter and in the layered medium are identical at the centers of the alternate layers. Transient waves in the layered medium are then obtained by solving the transient waves in the “equivalent” homogeneous viscoelastic medium. Solutions at points other than the centers of the alternate layers are also presented. Numerical examples are given for transient waves in an elastic layered medium due to a step load applied at one of the boundary while the other boundary is fixed. Comparisons with the exact solutions by the ray theory show that the present theory can predict very satisfactorily transient waves in a finite layered medium.