Piezoelectric T-Matrix Development and Multiple Scattering Analysis of Electroacoustic Wave Propagation in Thin Plates

Harvesting of acoustoelastic wave energy in thin plates and other structures is a promising new research direction for scavenging energy to power small sensors and devices. In particular, metamaterial-inspired harvesting concepts have shown strong potential for enhancing harvesting of acoustoelastic wave energy. In support of continued development of these metamaterial-based concepts, this paper presents a fully-coupled T-matrix formulation for assessing scattering of incident wave energy from a piezoelectric patch attached to a thin plate. The T-matrix serves as an input-output relationship between incident and reflected waves, and is developed herein for a piezoelectric patch connected to an external circuit. The utility of the T-matrix is evident in problems with multiple piezoelectric harvesters, where it can be used with other T-matrices (such as those previously formulated for rigid, void, and elastic inclusions) in a multiple scattering context. This has the potential for many uses in predicting the dynamic response of smart and active structures, but may be particularly useful in accurately assessing metamaterial-based energy harvesting enhancement strategies. Following development of the requisite T-matrix, harvesting in an example Gradient-Index (GRIN) metamaterial structure is predicted using the multiple scattering approach.