Finite element modeling of one-dimensional nonreciprocal acoustic metamaterial with anti-parallel diodes

A class of passive nonreciprocal acoustic metamaterials is developed to control the flow and distribution of acoustic energy in acoustic cavities and systems. Such development departs radically from present methods that favor the transmission direction by using hardwired arrangements of the hardware and hence, it cannot be reversed. The proposed nonreciprocal acoustic metamaterial (NAMM) cell consists of a cylindrical acoustic cavity with piezoelectric flexible boundaries that provide control in one-dimension. These boundaries are connected to an array of anti-parallel diodes to introduce simultaneous nonlinear damping and stiffness effects that break the reciprocity of energy flow through the NAMM cell. A finite element model of the NAMM cell is developed to investigate the nonreciprocal characteristics of the cell by optimizing the parameters that influence the nonlinear damping and stiffness effects introduced by the diodes. Numerical examples are presented to demonstrate the effectiveness of the proposed NAMM in tuning the directivity, flow, and distribution of acoustic energy propagating though the metamaterial.