| A theoretical study of dispersive nonlinear surface acoustic waves (SAWS) is performed. The dispersion is due to thin-film coating of a semi-infinite substrate. Both substrate and film materials are nonpiezoelectric elastic solids. Existing nonlinear evolution equations for SAWS are augmented to include the dispersion law obtained by solving the corresponding linear boundary value problem for a layered substrate. Numerical simulations are performed to study the evolution of both continuous and pulsed SAWs under the combined influence of nonlinearity and dispersion. Two isotropic substrate-film pairs are chosen which exhibit the two characteristic types of film dispersion, referred to as loading and stiffening dispersion. The specific materials considered for the study are a fused-quartz substrate coated with a gold film for loading dispersion, and an alumina film for stiffening dispersion. An extensive parametric study is undertaken for different strengths of nonlinearity, dispersion, and absorption. Waveform distortion is found to vary dramatically within this parameter space. Nonlinear SAW propagation in single-crystal silicon laminated with an oxide film is also investigated. Numerical predictions are compared with measurements provided by A. Lomonosov and P. Hess at the University of Heidelberg, Heidelberg, Germany. Theory and experiment show quantitative agreement. The existence of nonlinear stationary SAWs is considered. Both periodic and isolated stationary pulses are obtained numerically, and aspects of solitary wave behavior are examined. An analytic solitary-wave solution of the time-domain evolution equation is obtained for a Korteweg-de Vries approximation of the dispersion law. |
