Theoretical And Experimental Study On Influence Of Electrode Coverage On The Energy Harvesting Performance Of Piezoelectric Cantilevers

With the development of large-scale integrated circuit and wireless communication technology,wireless sensor networks are receiving considerable attention for the potential of improving our working and life styles.At present,wireless sensor nodes are mainly powered by battery.Due to the large quantity and wide distributions of sensor nodes,replacing batteries is always a heavy workload and costly.Own to the progress of energy collecting technique,energy harvester is promising to power sensor node sustainably,which is considered as a feasible alternative to battery.Among various energy harvesters,cantilevered piezoelectric energy harvesters(PEHs)based on vibration have received great attention in the last two decades owing to their large power density,ease of application,simple structure,and accessible large strain.Because the stress and strain on the cantilever beam are not uniform,parallel connections of different piezoelectric elements will reduce the overall average strain and affect the output performance.Therefore,the optimization of electrode coverage is of great significance to obtain the optimum output performance.Based on Euler-Bernoulli beam theory and the generalized Hamilton’s principle,a theoretical model for the forced vibration of piezoelectric cantilever beams with variable effective electrode coverage(EEC)is established in this work.Bidirectional electromechanical coupling,nonlinear stiffness,linear and nonlinear damping are fully taken into consideration.For the reduced linear model,multi-mode and singlemode analytical solutions are obtained from harmonic response analysis.For the nonlinear model,the numerical solution is obtained based on the harmonic balance method.The analytical solutions of the linear model indicate that the energy harvesting efficiency of PEH with different EEC is mainly influenced by the coupling strength.When the mechanical damping ratio is relatively low,both cantilevers with and without proof mass behavior as strongly coupled systems.The maximum output power firstly increases and then remains at a certain level with the increasing EEC.The optimal EECs of the PEHs are the EEC ranges higher than the critical EEC.When the mechanical damping ratio is relatively high,the maximum output power firstly increases and then decreases with the increasing EEC.The EECs obtaining the maximum effective electromechanical coupling coefficients are essential for maximizing the energy harvesting efficiency.To evaluate the coupling strength and power limit of nonlinear systems,equivalent effective electromechanical coupling coefficient and equivalent mechanical damping ratio are introduced.Numerical results show that the equivalences are effective for evaluating the coupling strength and the power limit.Under the same excitation level,the critical EECs of nonlinear beams are higher than their linear counterparts.Due to nonlinear damping,the power harvesting characteristics of nonlinear beams under different excitation levels are similar to the responses of linear beams with different damping ratios.The optimal EECs of weakly coupled nonlinear beams are almost the same as those of linear piezoelectric beams.To verify the theoretical model,piezoelectric beams with variable EEC are constructed using PZT and 304 stainless steel plates.A semi-automatic frequency scanning vibration platform is set up based on an electromagnetic shaker.The output power frequency responses of constructed beams with different EECs are tested.The experimental results agree well with the numerical results and the validity of the nonlinear model is verified.On the basis of the positive correlation between the near-open-circuit resonance frequency and the effective electromechanical coupling coefficient,a new frequency tuning method base on coupling adjustment is proposed.The effects on the resonance frequency shift of piezoelectric material,proof mass,and the laminated structure of the beam are studied using the linear models.The results show that the near-opencircuit resonance frequency of PEHs can be tuned by adjusting the EEC.Single crystals such as PMN-PT and PZN-PT are recommended for obtaining wider frequency shifts.The relative weight of the proof mass mainly affects the EEC where the maximum effective electromechanical coupling coefficient occurs.Proper proof mass ensures the monotonical increase of frequency shift with EEC.The optimal thickness ratio of the piezoelectric plate relative to the substrate is also helpful to improve the frequency shift.Broadband PEH based on PZT was achieved by coupling frequency tuning.The built-up bandwidth the average power in the effective frequency range are both improved,compared with traditional PEH with given EEC.Besides,a PEH constructed with PZN-PT obtained a frequency shift of 14.4% at EEC of 100%,indicating the potential of fabricating broadband coupling tuning PEHs with single crystals.