Verification of surface wave solutions obtained by the reciprocity theorem

•Surface wave motions generated by a time-harmonic point load are investigated.•Expressions for the displacements are determined by the reciprocity theorem.•Wave motions due to a horizontal load are obtained by the use of Hankel transform.•The solutions by using reciprocity, Hankel transform, and by...

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Bibliographic Details
Published in:Ultrasonics 2014-09, Vol.54 (7), p.1891-1894
Main Authors: Phan, Haidang, Cho, Younho, Achenbach, Jan D.
Format: Article
Language:English
Subjects:
Half-space
Hankel transform
Point load
Reciprocity
Surface wave
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Summary:•Surface wave motions generated by a time-harmonic point load are investigated.•Expressions for the displacements are determined by the reciprocity theorem.•Wave motions due to a horizontal load are obtained by the use of Hankel transform.•The solutions by using reciprocity, Hankel transform, and by Lamb are the same. 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.
ISSN:0041-624X
1874-9968
DOI:10.1016/j.ultras.2014.05.003