ASA 124th Meeting New Orleans 1992 October

3aPA2. On the existence of stationary nonlinear Rayleigh waves.

Mark F. Hamilton

Yuri A. Il'insky

Evgenia A. Zabolotskaya

Dept. of Mech. Eng., Univ. of Texas at Austin, Austin, TX 78712-1063

The existence of stationary nonlinear Rayleigh waves is investigated theoretically on the basis of a new model equation for the propagation of finite amplitude Rayleigh waves in isotropic solids [E. A. Zabolotskaya, J. Acoust. Soc. Am. 91, 2569--2575 (1992)]. The spectral components of the proposed stationary waveforms are governed by coupled quadratic algebraic equations that are similar in form to those used by Parker and Talbot [J. Elast. 15, 389--426 (1985)]. However, whereas the theoretical investigation of Parker and Talbot predicted the existence of stationary nonlinear Rayleigh waves, the present investigation does not, unless artificial constraints are imposed on the frequency spectrum. The constraints considered here consist of abrupt truncation or gradual amplitude shading of the spectrum. Examples of stationary waves that result from these constraints will be presented. Differences between nonlinearity in Rayleigh wave propagation in isotropic solids and nonlinearity in sound wave propagation in fluids will also be discussed. [Work supported by the David and Lucile Packard Foundation and by ONR.]