Nonlinear energy harvesting via an axially moving piezoelectric beam with both d ₃₁ and d ₃₃ modes

Piezoelectric energy harvesters (PEHs) in the literature typically operate with a single conversion mechanism (either d ₃₁ or d ₃₃); the output power, therefore, is limited, and not sufficient to sustainably energize low-power electronics. In this study, a nonlinear PEH with coupled d ₃₁ and d ₃₃ modes is designed and evaluated. An axially moving piezoelectric beam (AMPB) was applied to investigate the contribution of d ₃₁ and d ₃₃ to the output, and the critical parameters of the configuration were determined. A distributed parametric electromechanical model was established to characterize the non-linear dynamics of AMPB with d ₃₁ and d ₃₃ modes. The Galerkin approach and the harmonic-balance approach were employed conjointly to investigate the forced response of the energy harvesting system. The axial velocity’s effects upon energy harvesting were as well discussed. Comparison of the frequency response functions (FRFs) for voltage and power output between energy structures of d ₃₁ and d ₃₃ modes revealed several discrepancies. For instance, the voltage and power output of the d ₃₃ mode were greater than those of d ₃₁ mode for low frequencies, and the difference between the two modes decreased as the frequency increased. For the composite mode d ₃₁ and d ₃₃, under the same parameter conditions, the voltage and power output were greater than the output of any single mode. The analytical results were supported by a numerical method through the finite difference method. Both analytical and numerical results indicated the FRF could be increased by increasing the excitation amplitude, reducing the damping coefficient, or increasing the electrode spacing. The present study showed the efficiency of the use of the FRF using nonlinear transverse vibration of AMPB for d ₃₁ and d ₃₃ modes.