Energy Harvesting Characteristics of Preloaded Piezoelectric Beams Based on Multi-Scale Approach

Low frequency, broad bandwidth and adjustable frequency have always been adopted as crucial indexes to measure the performance of piezoelectric energy harvesters (PEHs). The axial preload is deemed as one of the effective ways to improve these indexes. To explore the effect of preload on the energy harvesting characteristics, the electromechanical coupling governing equations were derived based on the Euler-Bernoulli beam theory and Gauss Theorem. The asymptotically analytic solutions of the displacement, the voltage and the average output po-wer were obtained with Galerkin discretization and the multi-scale approach. Then, through theoretical analysis, this paper obtained the expressions of the short-circuit and open-circuit resonance frequencies, the open-circuit voltage amplitude, the optimal output power and the optimal load resistance. For the cantilever beam model, the validity of the theory was verified by numerical simulation. Finally, the influence of preload on open-circuit voltage and optimal output power was analyzed. The results reveal that the axial preload can improve the energy harvesting efficiency of piezoelectric cantilever beam. Compared with the case without preload, the resonant frequency decreases by 31.6%, the amplitude of open-circuit voltage increases by 120.8%, and the optimal output power increases by 40.0%, when the preload is 20 N.