CLOSED-FORM SOLUTIONS FOR FORCED VIBRATIONS OF CURVED PIEZOELECTRIC ENERGY HARVESTERS BY MEANS OF GREEN'S FUNCTIONS

This article investigates the forced vibrations of curved piezoelectric energy harvesters by means of Green's functions. The differential method is used to analyze the in-plane forces of the cantilevered piezoelectric energy harvester. According to the governing equations of motion, the electromechanical coupled Prescott models are derived based on the piezoelectric constitutive relations, which the circumferential forcing and the circumferential inertia term can be negligible, and a damping effect, radial damping, is taken into account. Utilizing the Laplace transform, the explicit expressions of the Green's functions of the coupled vibration equations can be acquired. On the basis of the superposition principle and the physical interpretation of Green's functions, the coupled system is decoupled and the expression of the output voltage can be obtained analytically. The present model for the curved beam can be readily reduced to straight beam. In the numerical sections, the present solutions are verified by the results in some published references. By comparing with the result of traditional straight piezoelectric energy harvesters model, the high energy harvesting efficiency of the curved piezoelectric energy harvesters model in the thesis is demonstrated. It is apparent that the present model has a wider range of application than the existing ones. The influence of radial damping, Young's modules of two materials and some other essential physical parameters on the evaluation functions for output voltage and resonant frequency are discussed. This research suggests that to make the electric power reach the maximum value, the optimal resistive load is 1 M\Omega; the elasticity modulus for both piezoelectric material and structure material have a profound effect on the resonant frequency. By replacing the base materials with lower modulus of elasticity, the phenomenon of high frequency resonance can be improved to make the curved piezoelectric energy harvesters adapt to more complex working environment. However, the energy harvesting efficiency of the structure will be decline.