Abstract
Mathematical modelling of the active feedback control of piezoelectric sandwich beams at large vibration amplitudes is developed. The proportional and derivative potential feedback controls via piezo-sensor and actuator layers are used. The dynamics of the sandwich beam are modelled by a nonlinear partial differential equation with feedback gain coefficients dependent. Based on Galerking's method, a second order nonlinear differential equation with strong nonlinearities is obtained. The method of multiple scales is used and the amplitude frequency and phase dependent relationships are derived. The feedback parameters' effects on the frequency, phase and time responses of sandwich beams under various types of boundary conditions are investigated. With respect to the system and on the feedback parameters, an instable zone in the upper nonlinear frequency branch can be obtained. Critical amplitude, frequency and phase values of the resulting instable zone are analytically given. The stability of the obtained solution is analyzed using static and dynamic criteria.