Scattering of plane elastic waves at rough surfaces. II

Abstract

This is a continuation of (l) on the two-dimensional problem of the diffraction of elastic waves by irregular surfaces. The effect of an irregular surface with an isolated irregularity like a trough or ditch on incident plane harmonic P-and S F-waves is discussed. The maximum depth of the ditch is assumed small compared to the wavelength of the incident wave.It is found that, when either a P-or an #F-wave is incident on such a boundary, besides the specularly reflected P-and S F-waves whose amplitudes are independent of the curvature of the surface there exist scattered waves travelling in various directions. In particular the diffracted zone contains the following second wave-types whose amplitudes are proportional to the depth of the ditch: (i) direct reflected P-and SVwaves, which at large distances appear to diverge from the point of intersection of the axis of symmetry of the ditch and the horizontal plane asymptotic to the boundary if the ratio of the wavelength of the incident wave to the half-width of the ditch is large. If the ratio is small these waves are reflected in the specular directions, (ii) A 'secondary $-wave' which finishes as P having travelled most of the way as an $F-wave. Its energy is confined to the neighbourhood of the free surface, (iii) A secondary P-wave which travels along the surface and finally emerges into the medium as an SV-w&ve at the critical angle for the medium, (iv) Rayleigh waves whose particle motion is in elliptic orbits.

Reflection and transmission of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic solid half-spaces

“…Asano (1960Asano ( , 1961Asano ( , 1966 also used the Rayleigh's method to address problems of reflection and refraction of elastic waves at a corrugated interface between two uniform elastic half spaces. Abubakar (1962a) and Dunkin and Eringen (1962) used the perturbation method to study the problem of reflection of body waves from a rough surface of a semi-infinite elastic solid. In perturbation method, the amplitudes of suCopy right c The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences.…”

Response of shear wave from a corrugated interface between elastic solid/viscoelastic half‐spaces

“…Many researchers have attempted many problems of reflection and refraction of elastic waves from irregular interfaces by using different techniques, i.e. Abubakar 16–18, Asano 19–21, Deresiewiez and Levy 22, Deresiewicz and Wolf 23, Dunkin and Eringen 24, Gupta 25, Kumar et al 26, Kuo and Nafe 27, Ogilvy 28, Rice 29, Singh and Tomar 30, 31, Tomar and Co‐workers 32–35.…”

Symmetric and anti-symmetric Rayleigh–Lamb modes in sinusoidally corrugated waveguides: An analytical approach

“…have been considered. The analytical solution of wave propagation in structures with non-planar boundaries and interfaces has been the topic of investigation in the last three decades (Abubakar, 1962;Nayfeh, 1974;Nayfeh and Kandil, 1978;Boströ m, 1983aBoströ m, ,b, 1989Standströ m, 1986;Fokkemma, 1980;Glass and Maradudin, 1983;El-Bahrawy, 1994a,b;Banerjee and Kundu, 2004;Nico et al, 2005). Recently non-destructive evaluation of different aerospace structures, components of integrated smart structures with non-planar boundaries and civil structural components (rebars, pipelines, etc.)…”