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

Abstract

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.

Characteristics of Acoustic Metamaterials

“…Reciprocity is a concept so natural that its validity is taken or granted in everyday lives. For example, when the neighbours can be heard through a common wall, it should be assumed that the reverse is equally possible [47,48].…”

Non-reciprocal piezoelectric metamaterials with tunable mode shapes

“…The approaches adopted to the break the reciprocity vary from simple passive approaches to the more imaginative active means. Distinct among the passive approaches are those including constitutive nonlinearity (Liang et al, 2009;Gu et al, 2016;Merkel et al, 2018;Petrover and Baz, 2020;Raval et al, 2020), momentum bias (Fleury et al, 2014;Liu et al, 2015;Liu et al, 2019;Wiederhold et al, 2019), and gyroscopic coupling (Attarzadeh et al, 2019). The performance characteristics of the passive NMM are enhanced by providing them with active control capabilities as proposed, for example, by Popa and Cummer (2014), Popa et al (2015), Trainiti and Ruzzene (2016), Nasser et al (2017), Baz 2018 and Baz 2019a), Yi et al (2019), Karkar et al (2019), Zhai et al (2019) and Goldsberry et al, 2019 andGoldsberry et al, 2020. Other interesting active control approaches to break the reciprocity include the use of virtual gyroscopic controllers (Baz, 2018;Raval et al, 2021;Baz, 2022; and by introducing a unique eigen-structure tuning controller (Baz, 2020a, Baz, 2020bZhou and Baz, 2021).…”