Broadband energy harvesting using nonlinear vibrations of a magnetopiezoelastic cantilever beam

Abstract This paper investigates the mechanical behavior of a unimorph piezoelectric cantilever beam with a tip magnet and nonlinear boundary conditions imposed by repelling permanent two external magnets, subjected to a harmonic base excitation for broadband energy harvesting. The energy harvester is modeled as an in-extensional beam with Euler-Bernoulli assumptions. The curvature and 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 numerical study is performed to reveal the influence of different parameters such as tip magnet, presence and absence of the external magnets, gap distance between magnets, mechanical damping ratio and external resistance load on the scavenged power from the nonlinear energy harvester. It is shown that the addition of two external magnets and a sufficient tip magnet, and proper gap distance between magnets significantly increases the power and the voltage. In addition, it is shown that considering geometric nonlinearity, for both in the absence and presence of the two external magnets, affect and broaden the frequency range. It is observed that gap distance between beams significantly affect the frequency range and hysteresis region of the broadband energy harvester. Energy conservation is examined in the absence of the mechanical damping ratio, 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 external magnets for different value of the tip magnet and gap distance and the optimum value of the resistance load is obtained for each system.