Multi-cell Active Acoustic Metamaterial with Programmable Bulk Modulus

Abstract

Considerable interest has been devoted to the development of various classes of acoustic metamaterials that can control the propagation of acoustical wave energy through these materials. However, all the currently exerted efforts are focused on studying passive metamaterials with fixed material properties. In this article, the emphasis is placed on the development of a new class of composite acoustic metamaterials with effective bulk moduli that are programmed to vary according to any prescribed pattern along the volume of the metamaterial. The composite consists of an acoustic cavity, which is coupled with an array of actively controlled Helmholtz resonator to enable the control of the effective bulk modulus distribution along the cavity. The theoretical analysis of this class of multi-cell composite active acoustic metamaterials (CAAMM) is presented and the theoretical predictions are determined when the Helmholtz resonators are provided with piezoelectric boundaries. These smart boundaries are used to control the overall bulk modulus of the cavity/resonator assembly through direct acoustic pressure feedback. The interaction between the neighboring cells of the composite metamaterial is modeled using a lumped-parameter approach. Numerical examples are presented to demonstrate the performance characteristics of the proposed CAAMM and its potential for generating prescribed spatial and spectral patterns of bulk modulus variation.