Nonlinear Vibratory Energy Harvesting Of One-dimensional Continua

This paper reports an analytical study of nonlinear vibration energy harvesting via one-dimensional continuums（two-span piezoelectric-beams,axially moving piezoelectric-beams and fluid-conveying piezoelectric-pipes）.The distributed parameter electromechanical model is applied to explore the nonlinear dynamics of one-dimensional continuums.The Galerkin method and the harmonic-balance method are applied together to find forced responses of the energy-harvesting system under the multi-field action.The influences of system parameters on energy harvesting are also explored.（a）For two-span piezoelectric-beams,the benefits of nonlinear interactive between buckled beam spans are explored,and the differences between the amplitude and voltage output frequency response functions（FRFs）of single-span,buckling and two-span piezoelectric beams configurations are revealed.For example,the voltage output FRF of the two-span buckled configuration is larger than that of the other two configurations at high frequencies,whereas at low frequencies,the voltage output FRF of two-span unbuckled configuration is larger than that of the other two configurations.A hybrid energy harvester is designed to combine the voltages of single-span buckled,two-span and two-span buckled piezoelectric beam devices for obtaining broadband voltages output;（b）For axially moving piezoelectric-beams,comparison of the frequency response functions（FRFs）for the voltage and power output between the energy structures of the d₃₁ and d₃₃modes revealed some differences.For example,the voltage and power output of the d₃₃ mode were greater than those of the d₃₁ mode for low frequencies,and the difference between the two modes decreased as the frequency increased.For the composite mode d₃₁ and d₃₃,under the same parameter conditions,the voltage and power output are greater than the output of any single mode,and the energy output of d₃₃ mode could be improved by increasing the electrode spacing;（c）For fluid-conveying piezoelectric-pipes,the complex dynamic behavior of fluid-structure interaction is considered,and the differences of amplitude,voltage,current and power output FRFs at different fluid velocity were contrasted.For example,as the flow velocity increased,the resonance peak moves towards the low-frequency direction,but the odd-mode resonance peak amplitude decreases,and the even-mode resonance peak amplitude increases.Finally,the analytical results are supported by numerical methods.Both analytical and numerical results demonstrate that the voltage,current and power output FRF for one-dimensional continuums could be increased by increasing the excitation amplitude and reducing the damping coefficient.