Nonreciprocal metamaterial with programmable nonlinear virtual resistors

Abstract

Emphasis is placed on the development of a class of active acoustic diodes and metamaterials in an attempt to control the flow and distribution of acoustic energy in acoustic cavities and systems. The proposed active nonreciprocal acoustic metamaterial (ANAM) cell consists of only one-dimensional acoustic cavity provided with active flexible boundaries. These boundaries are made from piezoelectric bimorphs with the inner layers which interact directly with cavity acting as sensors for monitoring the pressures of the propagating acoustic waves. The outer layers of the bimorphs provide the necessary control actions to an array of programmable nonlinear shunted resistors. These resistors are programmable and are designed in such a manner to introduce simultaneous nonlinear damping and cubic hardening stiffness effects. A lumped-parameter model of the ANAM cell is developed to control the nonreciprocal characteristics of the cell by the selection of the proper balance between the nonlinear damping and stiffness effects. Lyapunov stability criterion is used to generate the structure of such a balanced control strategy. The Harmonic Balance Method is used to predict the limit cycle behavior of the ANAM, the backbone characteristics and the stable limits of the control gains. Numerical examples are presented to demonstrate the effectiveness of the proposed ANAM in tuning and programming the directivity, flow, and distribution of acoustic energy propagating though the metamaterial.