Electromechanical Models For Two Kinds Of Piezoelectric Transducers And Their Applications In Energy Harvesting

The implement of “smart structures” requires four key elements,i.e.,sensors,actuators,control strategies,and power supply with conditioning electronics.Piezoelectric materials,especially piezoelectric ceramics,have long been used as sensors and actuators in the field of engineering.In recent years,the application of piezoelectric materials in ambient energy harvesting and acoustic power transfer also attracted researchers’ attention worldwide.According to the key elements of “smart structures”,piezoelectric materials have already played an important role in the implement of “smart structures”(as sensors and actuators);In the foreseeable future,piezoelectric materials will also make it possible to provide alternative power options beyond cables and batteries for “smart structures”,which will greatly promote the development of “smart structures” towards wireless and integration.It is not difficult to see that the studies on piezoelectric transducers will greatly promote the development of “smart structures”.Among various piezoelectric transducers,cantilevered and stacked configurations are the basic and most widely used ones.The present study concentrates on the establishment of refined electromechanical models for cantilevered and stacked piezoelectric transducers as well as the development of novel piezoelectric energy harvesters,and further explores the application of cantilevered and stacked piezoelectric transducers in energy harvesting.The main contents and corresponding contributions of the present study are drawn as the following:(1)The exact solutions of cantilevered piezoelectric transducers subjected to quasistatic loads are obtained based on the theory of piezoelectricity and elasticity in the present study,which could provide guidance and/or verification for the further dynamic modeling of cantilevered piezoelectric transducers.In the framework of the theory of elasticity,strict boundary conditions are required to be satisfied,which makes it very difficult to obtain exact solutions for problems.Especially when the shear force is involved,such problems with obtainable exact solutions are very rare.A piezoelectric bilayer cantilever is a basic configuration for cantilevered piezoelectric transducers.However,for a general piezoelectric bilayer cantilever with distinguished layer thicknesses and material parameters in different layers,the exact solutions for combined thermal,electrical and mechanical loads involving shear force haven’t been obtained yet.In the present study,based on the theory of piezoelectricity and elasticity,using Airy stress function method,the unified solutions for piezoelectric bilayer cantilevers are obtained in Chapter 2.The present unified solutions provide accurate results for general piezoelectric bilayer cantilevers subjected to complicated quasi-static loads including shear force,axial force,bending moment,external voltage and temperature change.The present unified solutions for general piezoelectric bilayer cantilevers could be simplified to the solutions of unimorph and bimorph cantilevers,and thus theoretically modified the solutions of unimorph and bimorph cantilevers obtained based on Euler-Bernoulli beam theory.Besides,it is found in the present theoretical results that no matter how thin the piezoelectric layer is,the electric field in the piezoelectric layer is not uniform but linearly distributed along the thickness direction as long as there is bending action involved in the cantilevered piezoelectric transducers.(2)An improved distributed parameter model for cantilevered piezoelectric transducers is proposed,which further modifies the key electromechanical characteristics of cantilevered piezoelectric transducers obtained based on traditional distributed parameter models.When it comes to the dynamic modeling of cantilevered piezoelectric transducers,especially cantilevered piezoelectric energy harvesters,the Euler-Bernoulli beam assumption is usually employed due to its simplicity and efficiency.In the existing distributed parameter models of cantilevered piezoelectric energy harvesters based on Euler-Bernoulli beam theory,a basic assumption for the electric field is usually introduced,i.e.,uniform electric field assumption.However,under the framework of Euler-Bernoulli beam theory,the uniform electric field assumption led to a critical problem,i.e.,the divergence of the electric displacement in the piezoelectric layer is not zero.Since the divergence of the electric displacement represents the free charge density,this is against a basic physical law,i.e.,the free charge in an insulator should be zero.In the present study,inspired by the quasi-static solutions of a piezoelectric bilayer cantilever proposed in Chapter 2,a refined non-uniform electric field consideration is introduced to improve the traditional distributed parameter model of cantilevered piezoelectric energy harvesters in Chapter 3.As the cantilevered piezoelectric energy harvester model could be easily simplified to an actuator model,the present energy harvester model could be considered as an improved distributed parameter model for cantilevered piezoelectric transducers,including cantilevered energy harvesters and cantilevered actuators.The present improved distributed parameter model modifies the electromechanical characteristics of cantilevered piezoelectric energy harvesters obtained using traditional distributed parameter model,including the bending stiffness,the resonance frequency,the open-circuit voltage output,the optimal circuit load resistance,and the optimal power output.(3)Fully coupled Electromechanical models for stacked piezoelectric actuators,stacked piezoelectric energy harvesters,and acoustic power transfer systems are established and experimentally verified.In the existing models for stacked piezoelectric transducers,especially fully coupled electromechanical models based on piezoelectric and elastic theory,the effect of boundary mass and/or boundary constraint is rarely studied.As we known,the boundary mass and/or boundary constraint are usually applied to stacked piezoelectric transducers in practical applications,especially in acoustic power transfer systems for large electrical output.In the present study,taking the boundary mass and boundary constraint into account,fully coupled electromechanical models for stacked piezoelectric transducers based on piezoelectric and elastic theory are established and experimentally verified.Three configurations are considered,i.e.,actuator model,energy harvester model,and acoustic power transfer model.As a relatively new research field,the electromechanical characteristics of an acoustic power transfer system require indepth study urgently.Subsequently,using the present proposed fully coupled electromechanical model,detailed numerical studies are conducted to reveal the influence of boundary conditions on the performance of an acoustic power transfer system.(4)A novel flex-compressive piezoelectric energy harvesting cell is proposed.An electromechanical model for the proposed energy harvesting cell is established,and a prototype is manufactured.Although stacked piezoelectric energy harvesters are suitable for large direct loads,the stack based piezoelectric energy harvesters with k N level load capacity and m W level power output are rarely reported in the existing literatures.In the present study,using the stacked piezoelectric transducers as the energy conversion core,a novel piezoelectric energy harvester named flex-compressive piezoelectric energy harvesting cell(F-C PEHC)is designed,theoretically analyzed,manufactured and experimentally tested.The present energy harvesting cell is mechanically assembled from independent components with no bonding layer,and every component is replaceable.Through a special flex-compressive design,the force transmitting structure ensures the stacked piezoelectric transducer is subjected to compressive stress during operation,which greatly enlarged the load capacity of the energy harvesting cell.With different key steel elements,both enhanced and weakened modes can be achieved.According to the experimental results,under a 4Hz harmonic excitation of 600 N,the maximum power output approaches 17.8m W.During the experiment,the maximum mechanical load including the pre-load approaches 2.8k N which is quite large but not the ultimate bearing capacity of the present energy harvester.Additionally,an insight of the interaction between two parallel connected F-C PEHCs sharing the same end is also carried out.(5)A theoretical model for a track structure with embedded F-C PEHCs subjected to moving loads is established,and corresponding theoretical electric output of the F-C PEHC is obtained.Base on Euler-Bernoulli beam theory and Winkler elastic foundation,considering the F-C PEHCs embedded in the sleepers,numerical simulation is conducted in Chapter 7 for the application of F-C PEHCs in railway systems.A mechanical model of the track structure combined with F-C PEHCs embedded in the sleepers is established,and the theoretical performance of F-C PEHCs under moving loads is obtained.The numerical results show that while a train with 5 cabins runs over the F-C PEHC at the velocity of 40m/s,both weakened mode and enhanced mode F-C PEHC could generate hundreds of milliwatts level energy,i.e.,0.49 W for the enhanced mode and 0.62 W for the weakened mode.The results demonstrated that the F-C PEHC has great potential in harvesting energy in railway systems,and may be utilized as an alternative power resource for the wireless sensor networks.