An application of the dynamic Betti-Rayleigh reciprocal theorem to moving-point loads in elastic media

Author:
R. G. Payton

Journal:
Quart. Appl. Math. **21** (1964), 299-313

DOI:
https://doi.org/10.1090/qam/155477

MathSciNet review:
155477

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Abstract | References | Additional Information

Abstract: Two problems connected with the transient motion of an elastic body acted upon by a moving-point force are solved by an application of the dynamic Betti-Rayleigh reciprocal theorem. This theorem, which is the analogue of Green's theorem for the scalar wave equation, permits the solution to be written as a single expression, irrespective of the value of the (constant) moving-force velocity . In particular, the displacement field in an infinite elastic body, due to a transient-point body force moving, in a straight line, is given in a simple form. Next the surface motion of an elastic half-space acted upon by a transient pressure spot moving in a straight line is analyzed for a material for which Poisson's ratio is one-fourth. The normal displacement is expressed in a simple manner, but the tangential displacement is quite complicated and is not fully expressible in terms of elementary functions. Singularities of the displacement fields are identified and discussed.

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Additional Information

DOI:
https://doi.org/10.1090/qam/155477

Article copyright:
© Copyright 1964
American Mathematical Society