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The Transition between Neumann and Dirichlet Boundary Conditions in Isotropic Elastic Plates

¹ Department of Mathematical Theory of Elasticity and Biomechanics, Saratov State University, 83 Astrakhanskaya St., Saratov 410026, Russia
² Department of Mathematical Sciences, SISCM, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK
³ School of Computing and Mathematics, Keele University, Keele, Newcastle, Staffordshire, ST5 5BG, UK

^* To whom correspondence should be addressed.

	Abstract

The transition from Neumann (traction-free) to Dirichlet (fixed-face) boundary conditions is investigated in respect of wave propagation in a linear isotropic elastic layer. Attention is focused on the implications of such a transition on the dispersion curve branches within the long-wave region. The formation of low-frequency band gap that is expected to exist in layers with Dirichlet boundary condition is shown to be caused by different mechanisms in anti-symmetric and symmetric cases. Certain implications to short-wave propagation in the layer are also investigated. The study includes both a numerical investigation and a multi-parameter asymptotic analysis.

Key Words: Layer, dispersion, long waves, asymptotics, thickness resonance

First published on March 20, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286509103781


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