Active control of nonlinear vibration of sandwich piezoelectric beams: A simplified approach

Nonlinear vibrations of piezoelectric/elastic/piezoelectric sandwich beams submitted to active control are studied in this paper. The proportional and derivative potential feedback controls via sensor and actuator layers are used. Harmonic balance method and the Galerkin procedure are adopted. A complex amplitude equation governed by two complex parameters is derived accounting for the geometric nonlinearity and piezoelectric effects. The nonlinear frequency and loss-factor amplitude relationships with respect to the gain parameters are obtained. The feedback effects are analyzed for small and large vibration amplitudes of sandwich beams. The frequency response curves are presented and discussed for various gain parameters.