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Title: Elastic waves trapped by a homogeneous anisotropic semicylinder

It is established that the problem of elastic oscillations of a homogeneous anisotropic semicylinder (console) with traction-free lateral surface (Neumann boundary condition) has no eigenvalues when the console is clamped at one end (Dirichlet boundary condition). If the end is free, under additional requirements of elastic and geometric symmetry, simple sufficient conditions are found for the existence of an eigenvalue embedded in the continuous spectrum and generating a trapped elastic wave, that is, one which decays at infinity at an exponential rate. The results are obtained by generalizing the methods developed for scalar problems, which however require substantial modification for the vector problem in elasticity theory. Examples are given and open questions are stated. Bibliography: 53 titles.
Authors:
 [1]
  1. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St.-Petersburg (Russian Federation)
Publication Date:
OSTI Identifier:
22365879
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ANISOTROPY; BOUNDARY CONDITIONS; DIRICHLET PROBLEM; EIGENVALUES; ELASTICITY; GEOMETRY; MATHEMATICAL SOLUTIONS; OSCILLATIONS; SCALARS; SURFACES; SYMMETRY; TRAPPING; VECTORS