Multimodal wave propagation in smart composite structures with shunted piezoelectric patches

Wave propagation in composite structures with shunted piezoelectric patches is investigated in this study. The wave finite element approach is first developed as a prediction tool for wave propagation characteristics such as dispersion curves in composite structures, and subsequently extended to consider shunted piezoelectric elements through the diffusion matrix model. A three-layered composite beam equipped with a pair of resistor–inductor shunted piezoelectric patches is modeled and analyzed carefully with these numerical techniques. Reflection and transmission coefficients of propagating waves in this smart composite structure are calculated, and the performance of shunted piezoelectric patches on the control of wave propagation is investigated numerically with the diffusion matrix model. Another finite element formulation, named modified wave finite element method, which is dedicated to the analysis of wave propagation in multilayered composite structures, is proposed and developed for considering piezoelectric elements in the structures. It is a dynamic substructuring technique that allows the dynamics of a typical layer cross section to be projected on a reduced local wave mode basis with appropriate dimensions. Results issued from this method are compared to those issued from the classical wave finite element and diffusion matrix model formulations to demonstrate the pertinence of the modelings.