Modeling and Stochastic Dynamic Analysis of a Piezoelectric Shunted Rotating Beam

Abstract

This work presents a variational based stochastic electromechanical coupling model for response analysis of a rotating cantilever beam with piezoelectric patches surface-mounted. The resonant shunt circuits are connected to the piezoelectric elements to reduce vibrations of some specific resonance frequencies. The deterministic equations of motion are derived by the generalised form of Hamilton’s principle for electromechanical systems and Rayleigh-Ritz modeling method based on the orthogonal polynomial bases, while the Penalty method is adopted to connect the beam and piezoelectric patches. The parameter uncertainties are taken into account in both the structural and electric components. The generalized polynomial chaos expansion (gPCE) is employed to represent propagation of parameter uncertainties and to estimate the statistical characteristics of the responses. Various results are presented and compared with the Monte Carlo simulation (MCS) in order to validate the efficiency of the proposed formulation. Uncertainty analyses are carried out to ascertain the effects of probabilistic parameters on the responses. The results reveal that both the structure and piezoelectric uncertainty can affect the vibration behaviors, and consideration of parameter uncertainties is needed in dynamic designs in order to minimise the vibration response at resonance frequencies.