Numerical investigation on the coupled vibrations of piezoelectric energy harvester with a liquid-filled proof mass

Replacing the solid tip mass of a piezoelectric cantilever beam with a liquid-filled mass can increase its frequency bandwidth due to the effect of nonlinear liquid sloshing. To investigate the coupled vibrations of the piezoelectric beam and the sloshing liquid, as well as their contributions to the output power, a coupled two-dimensional finite element method-smoothed particle hydrodynamics model has been developed in this study. Using this model, the dynamic behavior of a piezoelectric beam with a liquid-filled rectangular container as the tip mass, subjected to vertical harmonic excitation, has been investigated. The effects of parametric sloshing, excitation level, and geometric nonlinearity on the output voltages have been studied in detail. The simulation results indicate that: (a) the parametric sloshing in the liquid container exhibits subharmonic characteristics, which can be triggered by matching the excitation frequency to twice the natural frequency of the sloshing mode; (b) the piezoelectric beam exhibits subharmonic or harmonic oscillations at parametric resonance; (c) due to the effect of coupled vibrations, the energy harvester with a liquid-filled proof mass has a broader bandwidth compared to the traditional harvester; (d) the frequency response diagram of the output voltage shows multiple peaks at high excitation amplitudes, and the bifurcations are caused by parametric sloshing.