The work considers the propagation of small but finite amplitude Rayleigh-like waves on an elastic half space covered by a different elastic layer of uniform and finite thickness. It is assumed that the free boundary of the layered half space is free of tractions, and stresses and displacements are continuous at the interface between the layer and the half space. Then the nonlinear modulation of a group of surface waves centered around a wave number is examined by employing the method of multiple scales. It is shown that the first order slowly varying amplitude of the wave modulation is governed asymptotically by a nonlinear Schrodinger (NLS) equation. Then the dependence of the stability of the solutions and of the existence of solitary wave-type solutions of NLS equation on the nonlinear material parameters is investigated numerically for both hypothetical and real material models.
[1]
G. Maugin,et al.
On the stability of surface acoustic pulse trains in coated elastic media
,
2001
.
[2]
A. Mayer,et al.
DO SURFACE ACOUSTIC SOLITONS EXIST
,
1998
.
[3]
A. Porubov,et al.
Long non-linear strain waves in layered elastic half-space
,
1995
.
[4]
M. Teymur.
Nonlinear modulation of Love waves in a compressible hyperelastic layered half space
,
1988
.
[5]
角谷 典彦.
A. Jeffrey and T. Kawahara: Asymptotic Methods in Nonlinear Wave Theory, Pitman, Boston and London, 1982, x+256ページ, 24×16cm, 11,470円 (Applicable Mathematics Series).
,
1983
.
[6]
J. Ockendon.
ASYMPTOTIC METHODS IN NONLINEAR WAVE THEORY
,
1982
.
[7]
Alan Jeffrey,et al.
Asymptotic methods in nonlinear wave theory
,
1982
.