Attenuation of Lamb waves in coupled-resonator viscoelastic waveguide

Abstract

Guidance of elastic waves is one of the main applications of artificial crystal structures. The attenuation of the guided waves is, however, often overlooked, as most of the proposed waveguides only comprise ideal elastic materials. In this work, we study the propagation of evanescent Lamb waves guided in coupled-resonator viscoelastic waveguide (CRVW), with special attention to attenuation. CRVW is defined by considering a linear chain of coupled defect cavities in a phononic plate made of epoxy. The viscoelastic behavior of epoxy is characterized numerically by the Kelvin–Voigt (K–V) model. Based on finite element analysis, the complex band structure and the spectrum of frequency response function (FRF) are obtained. Due to viscosity, guided Lamb waves are spatially damped. Two theoretical models are devised to predict the displacement distributions inside and outside a bandgap for guided waves, respectively, considering either the first or the first two least evanescent Bloch waves identified in the complex band structure. A CRVW sample is fabricated and characterized experimentally by laser vibrometry. Evanescent Lamb waves are observed to be strongly confined along the waveguide and at the same time to decay rapidly along the waveguide axis. Experiments and numerical simulations are found to be in fair agreement. The present work is expected to inspire practical applications of highly confined viscoelastic phononic waveguides.