On Wave Modes With Zero Group Velocity in an Elastic Layer

Abstract

A study is made of time-harmonic wave modes in an elastic layer in plane strain with traction-free surfaces. It is demonstrated that, at points of the Rayleigh-Lamb frequency spectrum where the group velocity vanishes, there exist nonseparable time-harmonic modes in which the amplitudes of the displacements vary linearly in the direction along the layer. These modes are used to explain the terrace-like structure of the free-vibration frequency spectrum of a circular disk.