Transverse to longitudinal mode conversion via nonlinear inertial effects in a locally resonant metamaterial plate

Acoustic and elastic metamaterials have potential for tailoring wave propagation in ways beyond the capabilities of conventional materials and have been shown to exhibit a myriad of rich dynamical effects, such as negative effective properties, cloaking, extreme damping, and non-reciprocity. However, most of the existing literature has been focused on linear dynamics in which these behaviors are restricted to narrow frequency bands. More recently, nonlinearity has been investigated as a method of increasing this bandwidth, as well as a means to broaden the palette of available dynamics. Past studies on nonlinear acoustic and elastic metamaterials have demonstrated effects not easily accessible in the linear regime, including harmonic generation, mode hopping and conversion, tunable band gaps, chaos, and intrinsic localized modes. In this work, we present a model for a nonlinear elastic plate metamaterial that exhibits mode conversion between transverse and longitudinal waves. The mode conversion is enabled by cantilevered beam attachments undergoing large-angle out-of-plane oscillations. By analyzing the unit cell of this locally-resonant plate, we interpret the transverse-longitudinal coupling as a nonlinear, anisotropic effective mass density. The mode conversion effect is demonstrated via direct numerical simulations. [Work supported by NSF and ARL:UT.]