Rayleigh waves of arbitrary profile in anisotropic media

Abstract

The paper deals with surface wave propagation in an orthorhombic elastic half-plane. The general profile of the wave is considered, incorporating the anisotropy effects within the known representation in terms of a single plane harmonic function.

Asymptotic Theory for Rayleigh and Rayleigh-Type Waves

“…The surface wave eigensolution in terms of a single harmonic function has been recently derived in Parker (2013) for arbitrary anisotropy by means of the Stroh formalism. Here we present briefly a more explicit result obtained by Prikazchikov (2013) for an orthorhombic half-plane.…”

“…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.…”

“…The material in this chapter originates from the publications ; Kaplunov et al ( , 2006; Dai et al (2010); Kaplunov et al (2010); Erbaş et al (2013); ; ; Prikazchikov (2013); Erbaş et al (2014); Kaplunov et al (2014); Ege et al (2015); Kaplunov & Nobili (2015); Kaplunov et al (2016). We express our sincere gratitude to all the co-authors in the publications mentioned above, and also acknowledge fruitful discussions with P. Chadwick, Y. Fu, A.P.…”

Explicit Models for Surface, Interfacial and Edge Waves

“…We study the classical Rayleigh surface wave (Rayleigh 1885) along with Schölte-Gogoladze (Schölte 1949 andGogoladze 1948) and Stoneley (1924) interfacial waves, and the edge bending wave on a thin plate discovered by Konenkov (1960), relying on the methodology established in our recent publications (Kaplunov et al 2006, 2013, Dai et al 2010, Erbaş et al 2012. General formulations for homogenous surface and interfacial waves were also developed last years by Achenbach (1998), Kiselev & Rogerson (2009), Kiselev & Parker (2010), Parker (2012).…”

Rayleigh waves in nonlinear elasticity

“…These investigations deal with harmonic surface waves travelling along the traction-free flat surface of half-spaces. Surface waves with arbitrary profile as well as surface waves guided by topography and those traveling along forced surfaces have also attracted attention and we refer to Kiselev and Rogerson [56], Kiselev and Parker [57], Prikazchikov [58], Parker [59], Adams et al [32], Fu et al. [60], Kaplunov et al [61] and references therein.…”