Power enhancement of broadband piezoelectric energy harvesting using a proof mass and nonlinearities in curvature and inertia

Abstract This paper investigates the mechanical behavior of a unimorph piezoelectric cantilever beam with a tip mass subjected to a harmonic base excitation for energy harvesting. The energy harvester is modeled as an in-extensional beam with Euler–Bernoulli assumptions. The curvature and the inertia terms are assumed to be nonlinear due to large amplitude vibrations. The governing equations of motion are derived using the Euler–Lagrange equations. The reduced-order model equations (ROMs) are obtained based on the Galerkin method. A parametric study is performed to reveal the influence of different parameters such as proof mass, damping ratio and external resistance load on the scavenged power from the nonlinear energy harvester. It is shown that the addition of a sufficient large tip mass, significantly increases the power and the voltage. The effect of the tip mass on the Fast Fourier Transform (FFT) of the tip displacement and generated voltage is studied, and it is shown that in the presence of the tip mass two frequencies of the system are excited in contrast to the no tip mass case in which one frequency is excited. Furthermore, it is observed that the second excited frequency is three times of the first one, and due to the small amplitude ratios of the tip displacement of the second frequency to the first frequency, the second frequency can be neglected. Energy conservation is examined in the absence of the mechanical damping, and it is shown that energy harvesting annihilates the vibrations. In addition, the effect of the external resistance load on the average power is discussed in the presence and absence of the tip mass and the optimum value of the resistance load is obtained for each system. Some results obtained from MATLAB software were validated by using FE analysis with commercial software COMSOL, and a good accordance was shown between the results obtained from mentioned methods.