Nonlinear Rayleigh waves: Harmonic generation, parametric amplification, and thermoviscous damping

The propagation of surface acoustic waves in a nonlinear isotropic elastic material is investigated. The effects of heat conduction and viscous internal damping, both assumed small, are included. The method of multiple scales is used to investigate the slow modulation of a wave of arbitrary initial profile and a coupled system of integrodifferential equations is obtained for the variation of the different harmonic constituents. Explicit numerical solutions are obtained for the generation of higher harmonics by an initially sinusoidal wave and for the parametric amplification of a weak signal by a pump wave of twice the frequency.