Elastic wave propagation in locally resonant sonic material: Comparison between local interaction simulation approach and modal analysis

Abstract

Locally resonant sonic materials exhibit strong sound attenuation bands in the audible frequency range due to resonance scattering of elastic waves. We compare the results of a finite element modal analysis of a single resonant unit with sound attenuation spectra obtained from wave propagation simulations based on the local interaction simulation approach. The modal analysis yields a complete prediction of all resonance modes including information on node locations, mode degeneration, and modes that do not attenuate sound due to geometrical symmetries. Elliptical instead of circular inclusions break the geometric symmetry of the resonators, splitting the attenuation peak of degenerate modes into separate peaks. A small frequency shift is observed between the resonance frequencies and the frequencies of maximum sound attenuation, due to the asymmetric shape of the attenuation peaks and interference between resonance scattering and free propagating waves.