Numerical investigation of non-reciprocal wave propagation in mechanically-modulated elastic metamaterials

Abstract

Acoustic systems that break reciprocity have recently received great attention due to their potential to increase control over wave propagation and to have far-reaching impacts on engineering applications, including more efficient acoustic communication devices and vibration isolation. One means to break reciprocity is by spatiotemporal modulation of material properties, typically via electromagnetic actuation. In the present work, tunable mechanical metamaterials are investigated as a platform to achieve non-reciprocity, where effective dynamic property modulations are induced by an external pre-strain of a two-dimensional cellular material. These elastic metamaterials are studied using a nonlinear finite element model, which is suitable for unit cells having complex geometry and undergoing large deformation caused by the external pre-strain [Goldsberry et al., J. Appl. Phys., 123, 091711 (2018)]. A small-on-large approximation is used to analyze linear elastic, non-reciprocal wave propagation in the presence of a slowly-varying pre-strain. Results on non-reciprocal wave propagation in negative stiffness honeycombs, a structure exhibiting large stiffness modulations due to the presence of a mechanical instability [Correa et al., Rapid Prototyping J., 21(2), 193–200, (2015)], are shown as a case example. [Work supported by NSF.]