Stability analysis of active acoustic metamaterial with programmable bulk modulus

Abstract

Acoustic metamaterials (AMMs) have been considered as an effective means of controllingthe propagation of acoustical wave energy through metamaterials. However, most of thecurrently exerted efforts are focused on studying passive metamaterials with fixed materialproperties. In this paper, the emphasis is placed on the development of a new class ofone-dimensional acoustic metamaterials with effective bulk moduli that are programmed tovary according to any prescribed pattern along the volume of the metamaterial. Acousticcavities coupled with either actively controlled Helmholtz or flush-mounted resonators areintroduced to develop two possible configurations for obtaining active AMMs(AAMMs) with programmable bulk modulus capabilities. The resonators are providedwith piezoelectric boundaries to enable control of the overall bulk modulus of theacoustic cavity through direct acoustic pressure feedback. Theoretical analyses ofthese two configurations of AAMMs are presented using the lumped-parametermodeling approach. The presented analyses are utilized to study the stabilitycharacteristics of the two configurations in an attempt to define their stable regions ofoperation. Numerical examples are presented to demonstrate the performancecharacteristics of the proposed AAMM configurations and their potential forgenerating prescribed spatial and spectral patterns of bulk modulus variation.