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The Quarterly Journal of Mechanics and Applied Mathematics 1990 43(1):57-73; doi:10.1093/qjmam/43.1.57
© 1990 by Oxford University Press
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MODIFIED FUNDAMENTAL SOLUTIONS FOR THE SCATTERING OF ELASTIC WAVES BY A CAVITY

L. BENCHEIKH

( Department of Mathematics, University of Manchester Manchester M13 9PL )

Integral-equation methods are often used to treat the exterior problems of elastodynamics. It is known, however, that the simplest integral equations fail to be uniquely solvable at certain frequencies (irregular frequencies). Irregular frequencies are known to arise from the method of solution rather than the nature of the problem. Two methods for eliminating irregular frequencies are proposed. Both are based on modifying the fundamental solution. The first uses a dissipative type of condition on a boundary inside the scatterer. The second involves the addition of a finite series of multipoles with some suitable and mild conditions on the coefficients of these multipoles.


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