Dynamic Control of Piezoelectric Sandwich Beams with Multi-Frequency Excitations

In this work, we present a non-linear analysis of the dynamics of a sandwich beam with piezoelectric patches under multi-frequency excitations. The model takes into account geometrical non-linearities, piezoelectric non-linearities, and inertia. Hamilton’s principle is used to determine the electromechanical equation of motion, and Garlekin’s technique is used to determine the equivalent model of the piezoelectric generator. A mathematical methodology based on the multi-scale method for vibration control and stability is reviewed in this work to determine a system of amplitude and phase equations. The control of primary and secondary mode resonances is developed, and feedback effects are analyzed for small and large amplitudes of vibrations of sandwich beams. Frequency response curves are presented and discussed for various gain parameters.