Plane P- and SV- Waves in Inhomogeneous Elastic Media with Harmonic Variation of Density

Abstract

This paper considers propagation of plane P- and SV-waves in an inhomogeneous elastic medium with harmonic variation of density. By assuming a small inhomogeneity in the density and using the perturbation method of multiple scales, the wave propagation phenomenon is discussed within a frame of the first order solution. Three unstable(resonant) frequencies are found. Near the unstable region, the amplitude of an internally reflected wave is of the same order as that of the incident wave. However, the wave is stable when the amplitude of an internally reflected wave is a higher order of a small parameter or when the amplitude of an internally refracted wave is the same order as that of the incident wave. It is concluded that unstable wave propagation in the harmonically inhomogeneous elastic medium occurs when an internally reflected wave appears and then its amplitude increases to the same order as that of the incident wave.