General Elastic Surface Waves in Anisotropic Layered Structures

Rayleigh-type waves on a coated elastic half-space with a clamped surface

“…The effective boundary conditions can then be used to proceed with a specialized hyperbolicelliptic formulation for the studied Rayleigh-type waves, which was originally established in [16] using the symbolic Lourier approach (see e.g. [9] and references therein) and further developed in [17] starting from a slow time perturbation of the eigensolution for a homogeneous surface wave of arbitrary profile, see [18] and also earlier publications [19,20], as well as more recent papers including [21][22][23][24][25][26][27][28]. The general asymptotic methodology of extracting the contributions of surface, interfacial and edge waves from overall dynamic responses induced by prescribed loads is exposed in [29], with the effect of anisotropy addressed recently in [30].…”

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

“…The peculiarities of the procedure are clarified in Appendix A by a simple example of a single degree of freedom linear oscillator. In subsection 4.1 the 2D dynamic equations of the plane strain problem are perturbed around the eigensolution for a surface wave of arbitrary profile obtained in Chadwick (1976b), see also earlier papers of Friedlander (1948) and Sobolev (1937), as well as more recent publications, including Achenbach (1998); Kiselev (2004); Parker & Kiselev (2009) ;Kiselev & Parker (2010); Rousseau & Maugin (2011);Prikazchikov (2013); Parker (2013), and Kiselev (2015), treating homogeneous Rayleigh and Rayleigh-type waves in a more general setup. It appears that this eigensolution can be expressed in terms of a single harmonic function.…”