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

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 shortwave propagation in the layer are also investigated. The study includes both a numerical investigation and a multi-parameter asymptotic analysis.