Generation of the Third Harmonics by Plane Waves in Murnaghan Materials

We demonstrate that it is expedient to use the complete expansion of the potential in terms of strain gradients for materials whose deformation is described by Murnaghan’s potential. The cubic terms are retained in the constitutive equations, in addition to the classical quadratic terms. An analysis of the nonlinear system of wave equations reveals that the third harmonics can be generated. As an example, the nonlinear interaction of plane waves is analyzed for the following three cases of waves entering a medium: (i) a longitudinal wave, (ii) a vertically polarized transverse wave, and (iii) vertically and horizontally polarized transverse waves.