Multiple zero-group velocity resonances in elastic layered structures

Abstract

To date, the phenomenon of zero group velocity (ZGV) Lamb wave in a stress-free elastic plate has been well studied and used in non-destructive material characterization, electroacoustic devices and some other applications. This phenomenon is associated with the backward mode appearing in the range limited by the ZGV and cutoff frequencies. The modal frequency response of the structure, primarily the spectrum of the corresponding guided wave (GW) excited in the plate by a force source, is featured by a sharp peak at the ZGV frequency, allowing its experimental detection. Other peaks appearing at the cutoff frequencies indicate thickness resonances. In a layered half-space of infinite thickness, the backward-mode bend of the dispersion curve turns into a double bend that gives rise to three GWs associated with the same branch (one backward and two forward modes). Moreover, several adjacent branches with double bends, and, thus, several peaks, can appear in a narrow range as the number of layers increases, indicating multiple ZGV resonances. Such dispersion curves with double ZGV points were also found in waveguides of finite thickness with anisotropic or contrast material properties; however, their resonance manifestation is poorly studied. In this article, we consider and discuss several kinds of multi-peak ZGV responses using examples of layered samples of various materials. Along with the expected increase in the number of peaks in multilayer structures with contrast layers, it was noted that some ZGV points may or may not appear in peaks, depending on the type of load.