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Verification of surface wave solutions obtained by the reciprocity theorem
Haidang Phan1, Younho Cho1, Jan D Achenbach2
1School of Mechanical Engineering, Pusan National University, Busan 609-735, South Korea.
Ultrasonics
|June 15, 2014
Summary
This study simplifies calculating surface wave motion from point loads using the elastodynamic reciprocity theorem. The method yields results identical to traditional, more complex integral transform techniques.
Area of Science:
- Solid mechanics
- Elasticity theory
- Wave propagation
Background:
- Surface wave motion analysis typically uses complex integral transform techniques.
- Inverse transforms in these methods can be difficult and may not provide closed-form solutions.
Purpose of the Study:
- To present a simpler method for determining surface wave displacements from point-load excitation.
- To validate the efficacy of the elastodynamic reciprocity theorem in this context.
Main Methods:
- Application of the elastodynamic reciprocity theorem.
- Analysis of time-harmonic point load on an isotropic linearly elastic half-space.
Main Results:
- Expressions for surface displacements were derived using the reciprocity theorem.
- The derived amplitudes match those obtained via Hankel transforms and Lamb's classical work.
Conclusions:
- The elastodynamic reciprocity theorem offers a straightforward approach to analyzing surface wave motions.
- This method provides an alternative to complex integral transform techniques, yielding identical results.
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