Second harmonic generation and parametric excitation of surface waves in elastic and piezoelectric solids

Nonlinear electroelastic equations, quadratic in the small field variables, are applied in the analysis of second harmonic generation of surface waves in piezoelectric solids. Preliminary to the treatment of the anisotropic piezoelectric case, the more tractable problems of the second harmonic generation and parametric excitation of surface waves in isotropic elastic solids are treated. In all instances the solutions asymptotically satisfy the nonlinear differential equations and boundary conditions on the surface of the semi-infinite solid to a specified order in a small parameter. Since the equations are quadratic rather than cubic in the small field variables, only initial spatial rates of growth of the harmonically generated and parametrically excited waves are determined. Nevertheless, an extension of the analysis to enable the calculation of more than the aforementioned initial slopes is indicated. In the isotropic elastic case the solution for the second harmonic reveals, among other things, that the ratio of the dilatational to equivoluminal portions of the growing second harmonic is the same as in the input Rayleigh wave.