Stability analysis of active acoustic metamaterial with programmable bulk modulus

Acoustic metamaterials (AMMs) have been considered as an effective means of controlling the propagation of acoustical wave energy through metamaterials. However, most of the currently exerted efforts are focused on studying passive metamaterials with fixed material properties. In this paper, the emphasis is placed on the development of a new class of one-dimensional acoustic metamaterials with effective bulk moduli that are programmed to vary according to any prescribed pattern along the volume of the metamaterial. Acoustic cavities coupled with either actively controlled Helmholtz or flush-mounted resonators are introduced to develop two possible configurations for obtaining active AMMs (AAMMs) with programmable bulk modulus capabilities. The resonators are provided with piezoelectric boundaries to enable control of the overall bulk modulus of the acoustic cavity through direct acoustic pressure feedback. Theoretical analyses of these two configurations of AAMMs are presented using the lumped-parameter modeling approach. The presented analyses are utilized to study the stability characteristics of the two configurations in an attempt to define their stable regions of operation. Numerical examples are presented to demonstrate the performance characteristics of the proposed AAMM configurations and their potential for generating prescribed spatial and spectral patterns of bulk modulus variation.