Efficient and accurate analysis of locally resonant acoustic metamaterial plates using computational homogenization

Abstract

This paper introduces a computational homogenization framework for metamaterial plates consisting of locally resonant acoustic metamaterial (LRAM) unit cells. Based on the linearity assumption, the unit cell model is simplified through the superposition of long-wavelength (quasi-static) and local resonant eigenmode solutions. This method results in closed-form expressions describing the macroscale thin plate (shell) with enriched internal variable fields representing the amplitudes of the local resonant eigenmodes. The homogenized macroscopic shell model is implemented using isogeometric analysis, allowing for a straightforward handling of higher-order continuity requirements. Validation against fully-resolved direct numerical simulations (DNS) is conducted, showcasing the capability of the approach in computing the dispersion spectrum of an infinite LRAM plate, as well as performing frequency and time domain analyses of a finite LRAM plate. Results demonstrate that the homogenized enriched plate model accurately predicts wave attenuation within the frequency band-gaps, vibration modes, and wave propagation outside the band-gaps, achieving significantly reduced computational cost compared to DNS. The developed homogenization framework serves as a valuable computational tool for the analysis and design of LRAM panels of finite sizes and arbitrary shape under non-trivial excitations.