Broadband and tunable PZT energy harvesting utilizing local nonlinearity and tip mass effects

In this paper, a broadband piezoelectric energy harvester with an applied restoring force is studied. The restoring force is modeled as a spring in the boundary conditions of the system. The system is composed of a clamped-free beam with a tip mass which is supported by a spring at the free end. A piezoelectric layer is bounded to the upper surface of the beam and the system is exposed to an external harmonic base excitation. A nonlinear distributed parameter model of the harvester is derived using the Hamilton's principle utilizing the Euler–Bernoulli beam theory assumption. The nonlinear strain-displacement field is used to take the large transverse deflections effects into account. The reduced-order model is derived by implementing the Galerkin discretization method and the dimensionless form of the equations is used to analyze the system. The effect of the piezoelectric layer on the free vibrations of the structure is determined. Effects of tip mass and base acceleration on the frequency response of the system are investigated. The results show that, the tip mass can amplify the scavenged voltage and tune the resonance frequency. To study the influence of different types of the restoring force, linear, hardening, and pure nonlinear behavior are considered for the applied spring. The results demonstrate that by applying a pure nonlinear restoring force, the resonance bandwidth of the harvester increases which causes the harvester to generate energy in a larger frequency bandwidth and the output voltage increased remarkably in comparison to clamped-free energy harvester. This phenomenon enhances the harvester efficiency in the cases of the excitations with the time-varying frequency or the random excitations and the results in a broadband energy harvester. Finally, studying the frequency response curves for the different values of the spring location declares that, as the location of the attached spring changes, the nonlinear resonance frequency alters. The maximum increase in the bandwidth is accompanied by the case where spring is attached at the free end of the beam.