A viscoelastic plate model for a glued laminated circular plate in a piezoelectric energy harvester

An electromechanical coupling model is a fundamental tool to predict accurately the energy harvested by piezoelectric structures. A viscoelastic model is proposed to analyze a piezoelectric glued laminated plate harvester. In accordance with the Kelvin-Voigt relation and the von Karman plate theory, nonlinear electromechanical coupling governing equations are derived from the Newton-Euler method and the Gauss law. The Galerkin method is applied to obtain the discretized equations for the vibration around the non-trivial static equilibrium configuration produced by the structural weights. The harmonic balance method is employed to determined approximately the voltage and acceleration amplitude-frequency response with convergence considerations. The resulting amplitude-frequency responses agree well with those obtained from experiments. To understand the viscoelasticity effects, the amplitude-frequency response curves predicted by the viscoelastic model are compared with those predicted by the elastic model. The results demonstrate that viscoelastic damping contributes more significantly at the higher order modes and under the larger excitations. The proposed viscoelastic model is used to examine the effects of different parameters such as the steel ring radius, the concentrated mass, and the load resistance on the output power.