Simultaneous modeling of mechanical and electrical response of smart composite structures

A smart structural model is developed to determine analytically the response of arbitrary structures with piezoelectric materials and attached electrical circuitry. The equations of motion are formulated using the coupled piezoelectric formulations. However, rather than solving for strain and electric field, the proposed model solves for the strain and electric charge. The equations of motion are simplified for the case of a composite plate structure using a refined higher-order laminate theory; however, the model is applicable to most structural models. Additional degrees of freedom are then added to describe any attached electrical circuitry. A method is also presented for system simplification using the structural mode shapes and natural frequencies. Results are verified using experimental data for passive electrical shunt damping. The developed model results in a general framework that can be useful in solving a wide variety of coupled piezoelectric-mechanical problems addressing issues such as passive electrical damping, self-sensing, and electrical power consumption.