The Extension of a Superposition Principle to Wave Propagation in Nonhomogeneous Elastic Media

Abstract

In this paper a superposition principle is extended to examine the wave propagation problem in composite materials, which can be phenomenologically characterized as being nonhomogeneous- isotropic. The method is particularly useful for the analysis of stresses and displacements in such media with finite geometrical bounds. The existence of a superposition principle is first established and the resolution of the wave propagation problem in nonhomogeneous media into the solution of a static and dynamic eigen-value problem demonstrated. Finally, for purposes of illustration, a one-dimensional problem is solved and data are presented.