Flexural modes coupling in cantilever-type piezoelectric energy harvesters

Abstract

The ability to harness the waste mechanical energy and convert it into useful electrical power has made kinetic energy harvesters a promising candidate to provide an everlasting energy source for wireless autonomous devices. Nonlinearities, whether introduced deliberately for the sake of bandwidth broadening or present intrinsically, can highly influence the dynamic response and output power behavior of these type of energy scavengers. This paper aims to investigate the effect of nonlinearity on multi-mode vibrational response of a harvester composed of a cantilevered piezoelectric composite beam with an attached mass of finite dimensions. To that end, first of all a 3-DoF lumped parameter coupled electromechanical model of the device is developed through a comprehensive mathematical approach and its mode shapes and natural frequencies are calculated. The perturbation method of multiple scales is then applied to obtain the steady state solutions to the extracted order-reduced governing equations of the system. Results indicate that a harvester with a cubic attached mass exhibits a simple Duffing-type resonance as the excitation frequency falls in the vicinity of each natural frequency. That occurs while for a U-shaped mass the vibration modes would be coupled through occurrence of an internal resonance. In this latter case, both flexural modes of the piezoelectric beam are stimulated by a single frequency excitation and contribute to the power generation leading to an enhancement of the total output power which is the major advantage of the proposed design in this paper compared to the other existing energy harvesters. The frequency response curves of the output power are found to be composed of four branches and include Hopf bifurcations and instability regions. To verify the results obtained from the analytical approach, they are compared to a numerical solution where a good agreement is observed between them.