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Title: Three-dimensional edge waves in plates
Authors: Zernov, V
Kaplunov, JD
Keywords: Edge wave;Elastic plate;Variation;Eigenspectrum;Rayleigh–Lamb
Issue Date: 2008
Publisher: Royal Society Publishing
Citation: Proceedings of the Royal Society of London, Series A, 464: 301-318, Feb 2008
Abstract: This paper describes the propagation of three-dimensional symmetric waves localized near the traction-free edge of a semi-infinite elastic plate with either traction-free or fixed faces. For both types of boundary conditions, we present a variational proof of the existence of the low-order edge waves. In addition, for a plate with traction-free faces and zero Poisson ratio, the fundamental edge wave is described by a simple explicit formula, and the first-order edge wave is proved to exist. Qualitative variational predictions are compared with numerical results, which are obtained using expansions in three-dimensional Rayleigh–Lamb and shear modes. It is also demonstrated numerically that for any non-zero Poisson ratio in a plate with traction-free faces, the eigenfrequencies related to the first-order wave are complex valued.
Appears in Collections:Computer Science
Mathematical Sciences

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