Dispersion anomalies of shear horizontal guided waves in two- and three-layered plates

Abstract

The dispersion spectra of SH guided waves are studied both analytically and numerically for two-layered plates with a plane of propagation being the plane of transverse isotropy. The boundary-value problems are considered for a plate with free, clamped, or clamped/free surfaces. It is noticed that formally the problem is very similar to that for symmetric and antisymmetric Lamb waves in a homogeneous plate. On this basis the Mindlin’s approach of a bound grid is applied for an analysis. It is found that the studied spectra are characterized by the following specific features. They have two asymptotic levels ct1 and ct2 corresponding to the speeds of SH bulk waves in both layers. In the vicinity of the upper level (ct2) dispersion curves form a step-like pattern tending to ct2 in succession one by one with further going down to the lower asymptote ct1. Over the level ct2 there is a zone, where dispersion curves have a wavy form similar to that in spectra of Lamb waves in homogeneous plates. It is shown that the families of dispersion branches related to the boundary conditions of free and clamped surfaces cross each other at the same types of nodes of Mindlin’s grid as those for symmetric and antisymmetric Lamb waves in a free homogeneous plate. The tracing speed level v=v0 is found where the appropriate families of dispersion curves cross each other beyond the nodes of Mindlin’s grid. It is proved that the spectra of symmetric and antisymmetric SH guided waves in symmetric three-layered plates with free or clamped faces are described by the same four equations as for the studied two-layered plates with free, clamped, free/clamped or clamped/free surfaces.