Abstract
We consider the three-dimensional mixed boundary value problem in elasticity about time harmonic oscillations of a semi-infinite anisotropic cylinder. We show that for certain position and shape of the clamping zone of the surface the elastic wave is trapped; i.e., the problem admits a nontrivial solution with exponential decay at infinity or, conversely, the absence of the trapped wave is guaranteed on all frequencies. We state some open questions that concern similar spectral problems.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 1, pp. 160–174.
The author was supported by the Russian Science Foundation (Grant 17-11-01003).
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Nazarov, S.A. Trapping Elastic Waves by a Semi-Infinite Cylinder with Partly Fixed Surface. Sib Math J 61, 127–138 (2020). https://doi.org/10.1134/S0037446620010115
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DOI: https://doi.org/10.1134/S0037446620010115