Modelling of a rotating active thin-walled composite beam system subjected to high electric fields

Abstract

An electromechanical coupled theory is used to develop the equations of motion of a rotating thin-walled composite beam with surface bonded/embedded piezoelectric transducers. The higher order constitutive relations for the piezoceramic material are used to take into account the impact of a high electric field. In the mathematical model of the hybrid structure, the non-classical effects like material anisotropy, rotary inertia and transverse shear deformation as well as an arbitrary beam pitch angle are incorporated. Moreover, the model considers the hub mass moment of inertia and a non-constant rotating speed case. This approach results in an additional equation of motion for the hub sub-system and enhances the generality of the formulation. It is shown that final equations of motion of the hub–beam system are mutually coupled and form a nonlinear system of partial differential equations. Comparing to the purely mechanical model, the proposed electromechanical one introduces additional stiffness-type couplings between individual degrees of freedom of the system.