Active acoustic metamaterial with fractional derivative controller

Abstract

A class of active acoustic metamaterial (AAM) is presented. The proposed AAM consists of an acoustic transmission line connected in parallel to an array of Helmholtz resonators that are provided with actively controlled boundaries. In this manner, the AAM is in effect an assembly of periodic cells, each of which consists of a Helmholtz resonator connected in parallel to two sections of the transmission line. The two sections meet the Helmholtz resonator at its neck. The local control action at each Helmholtz resonator of a unit cell is generated by using a Fractional Derivative (FD) controller that relies in its operation on the measurement of the flow resulting from the deflection of the resonator boundary and the flow rates inside the two transmission line sections before and after the resonator. Such a single local control action is shown to be capable of controlling the local effective density and elasticity of each unit cell. A lumped-parameter model is developed to model the dynamics and control characteristics of the AAM under different gains and exponents of the FD controller. The model is exercised to demonstrate the ability of the FD controller in generating metamaterials with double negative effective density and elasticity over broad frequency ranges as compared to conventional Proportional and Derivative (PD) controllers. With such capabilities, the development of AAM with FD control action may provide viable means for generating desirable spatial distributions of density and elasticity over broad frequency band using a small number of control actuators.