Nonlinear characterization and performance optimization for broadband bistable energy harvester

Abstract

As two crucial indicators of bistable energy harvesting performance, band width and power amplitude are simultaneously investigated for obtaining the synergy effect. Toward this goal, a nonlinear electromechanical-coupled distributed-parameter model of the bistable piezoelectric energy harvester is established. Based on the electromechanical decoupled method, approximate higher-order analytical solutions of the beam displacement, harvested power and effective bandwidth are derived. The cubic-function discriminant of the analytical solution is introduced to determine the nonlinear excitation-frequency boundaries of multiple solutions and power peak. The stability of the multiple solutions is analyzed through Jacobi matrix of the modulation equation. Superharmonic resonance is notified. Upward and downward sweep experiments and numerical solutions of time history curves, phase portraits and power spectra confirm the analytical findings. To realize optimized broadband energy harvesting, the parametric study on the coefficients of the linear and cubic elastic external forces with the corresponding optimal load resistance is performed. For the nonlinear hardening case, more positive linear coefficient is preferred. For the nonlinear softening case, the cubic coefficient slightly larger than its optimal value is recommended at each given linear coefficient. By tuning the load resistance and linear and cubic coefficients of the external force, broadband bistable energy harvesting with optimized power is realized.