Parametric excitation analysis for system performance of piezoelectric energy harvesters

Abstract

Capitalizing on the advantages of parametric excitation and real-life low frequency vibration, the steady-state response of piezoelectric energy harvesting system composing of a cantilever beam with a tip mass and horizontal excitation at the fixed end is investigated. By applying Hamilton's principle, the nonlinear partial differential equation of a cantilever bimorph piezoelectric energy harvesting system with an additional tip mass is derived and analyzed. The cantilever is modeled as an axially non-elongated Euler Bernoulli beam with geometric and damping nonlinearities. By using the Galerkin method, the nonlinear partial differential equation is reduced to an electromechanical coupling system that governs a cantilever piezoelectric energy harvesting system with a tip mass under parametric excitation. The first-order resonance response of this harvesting system is studied by using the method of multiple scales. The analytical response expressions and first-order amplitude functions for vertical displacement, output voltage and output power are derived and analyzed. The influence of different impedance and tip mass on the piezoelectric energy harvesting system performance is summarized and concluded. For the parametric excitation system, the load resistance shows significant influence on the initial threshold of the piezoelectric energy harvesters under parametric excitation. For a short circuit, the initial threshold increases with increasing load resistance. For an open circuit, the initial threshold decreases with increasing load resistance. For an open circuit resistance or a short circuit resistance under parametric excitation, an increase in the end block mass effectively reduces the resonance frequency of the piezoelectric energy harvesters. Consequently, the energy harvesting bandwidth is increased, and the harvesting effect of the piezoelectric energy harvesters is enhanced. In this paper, a more accurate and practical theoretical model is established to predict the electromechanical coupling behavior of cantilever piezoelectric energy harvester under parametric excitation. Using this approach, it is possible to complement parametric and direct excitation such that the advantages of parametric excitation can be achieved. It is also significant to improve the energy conversion efficiency of energy harvesting system.