Stability of Surface Rayleigh Waves in an Elastic Half‐Space

This paper is concerned with nonlinear analysis for the propagation of Rayleigh surface waves on a homogeneous, elastic half‐space of general anisotropy. We show how to derive an asymptotic equation for the displacement by applying the second‐order elasticity theory. The evolution equation obtained is a nonlocal generalization of Burgers' equation, for which an explicit stability condition is exhibited. Finally, we investigate examples of interest, namely, isotropic materials, Ogden's materials, compressible Mooney–Rivlin materials, compressible neo‐Hookean materials, Simpson–Spector materials, St Venant–Kirchhoff materials, and Hadamard–Green materials.