Note A note on finite amplitude transverse waves in a thermoelastic solid

Summary. If thermal and mechanical coupling is neglected, there is a class of isothermal strain energy functions for isotropic compressible hyperelastic solids, that admits the propagation of a finite amplitude transverse wave, without a coupled longitudinal wave, and a subclass that admits the simultaneous propagation of an uncoupled finite amplitude transverse wave and a longitudinal wave 1]. Several examples of this class of strain energy function are discussed. When thermal and mechanical coupling is considered the solid is described as thermoelastic. The purpose of this paper is to investigate the possibility of the propagation of a finite amplitude transverse wave without a coupled longitudinal wave, or the uncoupled simultaneous propagation of a finite amplitude transverse wave and a longitudinal wave, in an isotropic thermoelastic solid that has no underlying deformation. It is shown that an extensive class of isotropic thermoelastic solids does not admit the propagation of an uncoupled finite amplitude transverse wave, with or without an uncoupled longitudinal wave, even if the corresponding hyperelastic solid does.