Plate theory based modeling and analysis of nonlinear piezoelectric composite circular plate energy harvesters

A piezoelectric composite circular plate energy harvester is modeled and analyzed based on a nonlinear plate theory. The harvester consists of a bimorph piezoelectric circular plate and a rigid body. The nonlinear electromechanical coupling equations are derived from the Hamilton principle and the von Karman plate theory with the account for the structural weight. The equations are discretized via the Galerkin truncation method (GTM) for the vibration around the equilibrium configuration. The discrete equations are approximately solved via the harmonic balance method (HBM) with the convergence considerations. Moreover, the solutions are validated by the Runge–Kutta method (RKM) and the finite element simulations. The account for the structural weight leads to the asymmetricity in the relation of the restoring force and the deformation. The amplitude-frequency response curves display a typical hardened nonlinear behavior in the first-order vibration mode and a linear behavior in the second-order vibration mode. Parametric studies demonstrate the effects of the rigid body mass, the external excitation amplitude, the load resistance, and the piezoelectric composite plate size on harvesting the performance.