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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