Elastic and sound orthonormal beams and localized fields in linear media: III. Superpositions of transverse elastic plane waves in an isotropic medium

Abstract

Unique families of time-harmonic orthonormal beams and localized fields in an isotropic linear elastic medium are presented. They are obtained using expansions in transverse plane waves whose intensities and phases are specified by the spherical harmonics. The families of orthonormal beams can be used as functional bases for complex elastic fields. As in the case of fields formed from longitudinal plane waves, the presented localized fields include elastic storms, whirls and tornadoes. The orthonormal beams and the localized fields are illustrated by calculating fields, energy densities and energy fluxes.