Verification of surface wave solutions obtained by the reciprocity theorem

Haidang Phan; Younho Cho; Jan D Achenbach

doi:10.1016/j.ultras.2014.05.003

Verification of surface wave solutions obtained by the reciprocity theorem

Ultrasonics. 2014 Sep;54(7):1891-4. doi: 10.1016/j.ultras.2014.05.003. Epub 2014 May 15.

Authors

Haidang Phan¹, Younho Cho², Jan D Achenbach³

Affiliations

¹ School of Mechanical Engineering, Pusan National University, Busan 609-735, South Korea.
² School of Mechanical Engineering, Pusan National University, Busan 609-735, South Korea. Electronic address: mechcyh@pusan.ac.kr.
³ McCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL 60208, USA.

PMID: 24928810
DOI: 10.1016/j.ultras.2014.05.003

Abstract

Surface wave motions generated by a time-harmonic point load applied at the surface of an isotropic linearly elastic half-space are conventionally solved by the use of integral transform techniques. The inverse transforms, are often complicated and will not always yield closed-form solutions. In this paper expressions for the displacements for surface wave motions radiated from point-load excitation are determined in a simple manner by the use of the elastodynamic reciprocity theorem. It is shown that the radiated amplitudes of the surface displacements obtained by the reciprocity approach are identical to the corresponding results obtained by the use of Hankel transform and by Lamb in his classical paper.

Keywords: Half-space; Hankel transform; Point load; Reciprocity; Surface wave.