Study on the vibration suppression of beam structures with nonlinear piezoelectric shunt damping

Abstract

The vibration suppression of the nonlinear beam structure under harmonic excitations by employing the nonlinear piezoelectric shunt damping circuit (PSDC) is researched. The energy approach is utilized to deduce the dynamic equations of the nonlinear beams with nonlinear PSDC. The complexification-averaging approach and pseudo arc-length continuation approach are applied to calculate the frequency domain response of the beam structure. Numerous numerical examples are conducted to verify the present formulations, thereby demonstrating the remarkable efficiency and accuracy. The impacts of several parameters of the proposed PSDC are discussed and the optimal study of the nonlinear PSDC is further performed to obtain the optimal negative and nonlinear capacitances. The comparisons concerning the vibration of the beam structures with and without PSDC are implemented to examine the vibration mitigation performance of the designed PSDC. In the end, the design criterion of the nonlinear PSDC is given.