Studies On Nonlinear Bistable Piezoelectric Cantilever Vibration Energy Harvesting

Due to the advances in microelectronics and wireless technology in the past decades,wireless sensor networks and handheld electronic devices have become miniature and lowpowered.These devices are typically powered by conventional batteries(Ni-MH,Li-polymer,etc.).However,conventional batteries have lots of defects when using in these devices.Firstly,bulk of conventional batteries restrict the microminiaturization of microelectronics.Secondly,the life of batteries is limited and need to be recharged or replaced after a period of use,which makes it really hard for wireless sensor networks placed in harsh environments or remote areas.Considering this,a renewable alternative to batteries for the use of power supply for low-power electronics such as wireless sensor networks and self-sustained electronic components has been discovered utilizing the conversion of dispersed energy from ambient sources into electrical energy.Vibrational energy harvesters convert vibration energy into electrical energy to power wireless and Micro Electromechanical Systems(MEMS)devices.Among various renewable forms of energy,mechanical vibration is deemed to be one of the most attractive power sources for low-power and self-sustained electronics,owing to its power density,versatility,and abundance in real environments.Piezoelectric conversion mainly uses the piezoelectric effect,a unique property of piezoelectric crystals which will generate electrical charge if subjected to mechanical stress or vibration.The piezoelectric energy harvesting has the advantages of high energy density,simple structures,and ease of being embedded in MEMS.The conversion of mechanical energy from ambient vibrational energy into electrical energy via piezoelectric effect is particularly effective.Piezoelectric ceramics is one type of polycrystals that have piezoelectric properties.Among many,PZT is the most commonly used piezoelectric material for energy harvesting,especially in MEMS.PZT has an advantage of high piezoelectric constant and electromechanical coupling coefficient,well fabrication process,good structural compatibility with MEMS,and low cost.Due to this,piezoelectric energy harvesters using PZT have great advantages of high energy density,simple structures as well as easy miniaturization,resulting in wide applications in MEMS.Since linear-type cantilever structures have the advantages of producing the greatest deflection and compliance coefficient,having a lower resonant frequency with a wide dynamic range,having a low degree of structural steel,high sensitivity as well as being easy to be miniaturized,piezoelectric cantilever beams become the preferred structures applying in vibration energy harvesters.A conventional linear piezoelectric energy harvesting(PEH)prototype is typically based on a cantilever attached with piezoelectric patches and a tip proof mass.The cantilever structure is utilized to incur deformation of piezoelectric ceramics for electric charge generation while the proof mass aims to decrease the inherent frequency for environmental catering,since it requires the linear PEH to be under resonance for optimal oscillations to occur.A linear piezoelectric cantilever energy harvester performs best when the frequency of the ambience is exactly the same as its resonance frequency.Since ambient vibration energy is distributed over a wide spectrum and it is often located below a few hundred hertz with variable intensity,the performance of linear energy harvesters will be significantly affected when excited at broadband vibrations.This narrowband disadvantage,as a result,restricts the applications of linear energy harvesters in many realistic environments.In vibration harvesting,conventional linear energy harvesters are typically mechano-electrical resonant devices tuned with the dominant vibration frequency.Under ambient sources such as frequency-varying or random vibrations this solution is suboptimal because of the narrow frequency bandwidth of the converter.Due to the geometric constraints of space and dynamics,linear piezoelectric cantilever vibration energy harvesters can not meet the requirement of random unknown environmental vibration energy harvesting.To overcome the defects of linear piezoelectric cantilever vibration energy harvesters,nonlinear piezoelectric cantilever vibration energy harvesters become a research hotspot.It is demonstrated that nonlinear vibration energy harvesters perform better in vibration energy harvesting compared to linear devices by ranging over a wide spectrum.Many methods have been explored by several research groups to broaden the usable bandwidth of linear harvesters,including multi-modal oscillators,oscillator arrays,and active or adaptive frequency-tuning methods.While providing improvements,more advanced solutions were desired for broadband performance,and subsequently the exploitation of nonlinear dynamic phenomena became a focus of this research.Other than these methods,nonlinear PEHS appeared to realize effective broadband response.To date,researchers have exploited various approaches to introduce nonlinearity into energy harvesting for theoretical analysis and application exploration,including monostable Duffing,bistable oscillators,etc.Typical approaches to generate bistability are mainly based on magnetic attraction,magnetic repulsion,buckled beams and bistable plates.Recent research investigations find out that nonlinear vibration energy harvesters perform better in vibration energy harvesting compared to linear devices under broadband excitations while obtaining maximum power output.It has been proved that the maximum power output of nonlinear vibration energy harvesters under random excitations are 4-6 times that of linear counterparts,which indicates the superiority of nonlinear vibration energy harvesters.Among current nonlinear oscillator investigations,bistable energy harvester oscillating between two potential wells has been attracting lots of interests.Bistable oscillators have a unique doublewell restoring force potential which leads to optimal displacement and electric output.Among many alternatives,there are two general methods in realizing the double-well potential for the bistable configuration.One approach utilizes magnetic repulsion or attraction force to create bistable dynamics;the other magnetic-free approach is based on a buckled beam subjected to certain elastic boundary conditions or a near buckling vertical beam with certain tip mass.Among the current nonlinear oscillator investigations,bistable dynamics caused by magnetic repulsion has been attracting much interest.A conventional bistable magnetic repulsive piezoelectric energy harvester is composed of a piezoelectric cantilever with an internal magnet fixed to its free end and an external rigidly supported repulsive magnet,which contributes in forming two wells for bistable oscillations.With respect to the vibration source,filtered Gaussian noises or pink noises are normally used to simulate the ambience where the piezoelectric energy harvester(PEH)would be set up.These types of noises have common low-frequency features that make them proper candidates to simulate ambient noises.Rather than the filtered Gaussian noises,pink noises,whose power spectral density is inversely proportional to the frequency,are known to be similar to realistic ambient noises because their feature can also be generally found in ambient signals.However,pink noises with standard spectral representation can only be used for simulation of excitations assumed to possess constant intensity,whereas realistic ambient noises normally appear with random spectrum and varying intensity in terms of different locations and time.Unfortunately,the output performance of conventional bistable magnetic repulsive energy harvesters would be significantly affected by the ambience intensity.Insufficient intensity may lead to weak oscillations limited in either well instead of bistable transition oscillations between two wells,which would eventually result in insufficient energy harvesting.To overcome this defect of the conventional Rigidly Supported Piezoelectric Energy Harvesting System(RPEHS),an Elastically Supported Piezoelectric Energy Harvesting System(EPEHS)with an elastically supported model was firstly developed in this work to guarantee persistent bistable oscillations under varying-intensity excitation conditions.The EPEHS is composed of a piezoelectric cantilever with an internal magnet,which is fixed at its free end,an elastically supported external magnet,and a base,which is excited by ambient vibrations.With respect to the cantilever,we use a metal plate as substrate,while on both the substrate surfaces,PZT are deposited to perform the energy conversion.The piezoelectric bimorphs are of the same thickness and connected in series.The two magnets are mutually exclusive,forming a bistable system.The principle of the converter is that when excited by ambient sources,the oscillations of the piezoelectric cantilever would lead to deformations of PZT films,thus the conversion of mechanical energy from background vibrations into electrical energy via piezoelectric effect can be achieved.The difference between this model and a conventional rigidly supported model would be the fact that the external magnet is elastically supported,which is realized by a cantilever to ensure maximum vertical motion of the external magnet.Here we assume only vertical movements of the external magnet without considering swing motions in horizontal direction.This improved model not only retains vibration bistability of the piezoelectric cantilever but also introduces bistability into the external magnet's vibration characteristics,which consequentially creates an opportunity for the reciprocating transition oscillations of the cantilever.Note that when the system is at the equilibrium position,the effect of the two magnets' gravity on the static deformation of the piezoelectric cantilever beam and the spring is not considered.Meanwhile the internal magnet is located along the horizontal extension line of the cantilever while the two magnets are horizontally aligned.The system's variable potential function helps create an opportunity for the reciprocating transition oscillations of the cantilever,thus enhancing the transition probability and frequency.When excitation intensity is insufficient,thanks to the system's variable potential function,frequent bistable transition oscillations between two wells occur in the EPEHS,while only weak oscillations in either well could be observed in the RPEHS.If considered remaining the magnet interval and the spring's elastic stiffness unchanged while receiving stable maximum output voltage,the EPEHS can be made full use toward variable-intensity filtered Gaussian noises.The EPEHS has better power output performance than the RPEHS under low-intensity filtered Gaussian noises,while no matter under high-or low-intensity pink noises,the EPEHS always outperform the RPEHS,indicating the superiority of the EPEHS under realistic circumstance.It is demonstrated that the EPEHS are capable of adapting to random excitations with variable intensity,through which maximum power output and sufficient electromechanical energy conversion of the system can be accomplished.One typical approach to realize this elastically supported model is to support the external magnet by a cantilever.Under such condition,it can be easily proposed to deposit PZT onto the external cantilever for appropriate electromechanical energy conversion as well.Therefore,a Dual-Piezoelectric-Cantilever Energy Harvesting System(DPEHS)model is developed in the present study to achieve optimal broadband energy harvesting under varying-intensity realistic circumstance.It has already been proven that EPEHS is adaptive to filtered Gaussian noises or pink noises with variable intensity.On this basis,we went through a variety of realistic ambient conditions in this work to use as excitations to observe the energy harvesting performance of DPEHS for theoretical and applied study.The EPEHS has been verified to be more adaptive to realistic ambience with significant or medium intensity variation.The EPEHS is less qualified to realistic ambience with constant intensity than the RPEHS.Fortunately,the DPEHS is superior to the RPEHS under all circumstances owing to the dual piezoelectric cantilevers being efficiently utilized for electromechanical energy conversion to achieve optimal energy harvesting.A comparison of the rms of output voltage and acceleration values for the three structures in the horizontal and vertical placement reveals several conclusions.Acceleration of the substrate by external excitations in the vertical displacement is less than that in the horizontal placement.Output voltage of the EPEHS is optimal.In addition,the output voltage of the EPEHS varies with the intensity of the external excitations following corresponding trends,which is consistent with our observations at the experimental site.When displaced horizontally,the linear PEHS is superior to the RPRHS,while when displaced vertically the RPEHS is superior to the linear PEHS,which indicates that the superiority of the RPEHS may be only in the cases with low excitation intensity.In this work,we firstly introduced the research background and significance,revealed the current research status review,and illustrated the mechanism of the PEHS.Based on this,we established mathematical models for a RPEHS,an EPEHS and a DPEHS with subsequent dynamics analysis.The energy harvesting efficiency was analyzed by numerical simulation methods.The comparative analysis was then carried out.In order to validate the conclusion of the analysis,we established an experimental model for each system to verify the conclusions of numerical simulation.Finally,we proposed the future research plans and prospects based on current research.