Inhomogeneous Plane Waves in Incompressible Elastic Materials

Abstract

This chapter discusses inhomogeneous plane waves in incompressible elastic materials. Gibbs bivectors are used to give a description of inhomogeneous plane waves in anisotropic homogeneous incompressible linear elastic materials. It is shown that if the slowness bivector is not isotropic then the acoustical tensor has double roots if a circularly polarized wave propagates, and conversely, if the acoustical tensor has double roots then the corresponding wave is circularly polarized. The superposition of the displacements corresponding to the pair of waves with given directional ellipse is also presented in the chapter. For motion parallel to the plane of the amplitude bivector of either wave, it is seen that for equidistant points on certain lines the total displacement ellipses are similar and similarly situated with respect to each other and with respect to the projection of the slowness bivector onto the plane of the amplitude bivector.