Dynamics And Coherence Resonance Of Nonlinear Energy Harvesting System

With the development of microelectronic mechanical technology and precision manufacturing technology,modern micro-electric device and its application are widespread day and day.At present,most of these microdevices are powered by chemical batteries.However,the batteries have some disadvantages,such as limited lifespan,environmental pollution and need replaced periodically.Focusing on the energy conversion of ambient vibration energy,this paper investigated piezoelectric energy harvester,its conversion efficiency and improvement.In the initial stage,conventional vibration energy harvester usually uses linear resonance to extract energy.These kinds of harvesters were well suited to a narrow band frequency.In practice,the ambient excitation is generally non-periodic,random,low frequency and broadband,thus it is hard for the linear system to work efficiently.Since bi-stable energy harvesters could produce larger amplitude oscillation under random excitation,it is considered to be an efficient configuration to realize more energy conversion.A variety of methods,such as theoretical analysis,numerical simulation and experimental verification,are employed for investigating the response characteristic of nonlinear energy harvesting system.Some new types of energy harvesters are designed,the stochastic dynamic behaviors under random excitation are investigated.The electromechanical coupling governing equations are derived based on the Hamilton's principle;the homoclinic bifurcation of energy harvesting system under base excitations and parametric excitations are analyzed via the Melnikov method.The stochastic resonance and coherence resonance in bistable energy harvester or multi-stable energy harvester are proved by stochastic linearization method and verified through Monte Caro simulations.The main research works and results in this thesis are as follows1.Analytical studies were carried out to investigate the effects of homoclinic bifurcation on directly excited energy harvesters and parametrically excited energy harvesters.First the electromechanical coupling equations were derived by Newton's second law and Kirchhoff voltage law.The energy harvesting system can be regarded as a Hamilton conservative system under the disturbances of damping,electromechanical coupling and external excitation.From the Melnikov method,the criteria of homoclinic bifurcation are derived.The electromechanical model for the energy harvester under parametric excitation is established using the extended Hamilton's principle.The Melnikov function of this model is derived,and the necessary condition for occurrence of homoclinic bifurcation is presented.The results of analytical analyses can be used for optimization of the parameters of frequency and resistance.Experimental tests confirm that a wider frequency range of inter-well motion could be achieved at a larger initial distance.2.The equations for a SDOF lumped-parameter electromechanical coupling model were derived via Newton's second law and Kirchhoff voltage law.A closed-form approximation expression for calculating the ensemble average harvested power is derived.Numerical simulations reveal that the time constants in electrical circuit can affect the voltage produced,decreasing which will increase the harvested power.Secondly,we investigate the coherence resonance of this model by introducing a fractional damping,which is proved to be more accurate recently.It can be concluded that the reduction of fractional order not only reduces the critical value of excitation level that leading to coherence resonance,but also increase the amplitude on the occurrence of coherence resonance.Finally,we presented a novel hybrid energy harvester integrated with piezoelectric and electromagnetic effects.The experimental results show that the hybrid energy harvesting system has a better scavenging performance compared with the system only considering the piezoelectric or magnetoelectric effect.3.In order to gain insight into the influence of the harvester parameters on the output voltage,a distributed-parameter model of a clamped-clamped piezoelectric beam is established by using generalized Hamilton's principle.When the axial load is a static force,the response under harmonic base excitation experiences a period-doubling bifurcation as the frequency varies.Especially coherence resonance occurs when the system is subjected to a Gaussian random excitation.When the axial load is a harmonic one,the analytical study show that stochastic resonance can occur in the bistable mechanical system and thus harvest energy at a high efficiency.4.In order to improve the transform efficiency of the bi-stable energy harvester(BEH),we proposed an advanced bi-stable energy harvester(ABEH).First,the mathematical model is established and its dynamical equations are derived.It is shown that in ABEH the potential energy barriers is reduced and the snap-through is easily to occur between potential wells.To demonstrate the ABEH's advantage in harvesting energy,comparisons between the ABEH and the BEH are carried out for both harmonic and stochastic excitations.Our results reveal that the ABEH's inter-well response can be elicited by a low-frequency excitation and thus the harvester attains frequently jumping between potential wells at the fairly weak random excitations.Therefore it can generate a higher output power.5.To further reduce the barrier of potential energy and improve the efficiency of energy harvesting,we developed a tri-stable energy harvester(TEH).The formula of magnetic repulsion shows that with the increase of magnet distance,gradually the bi-stable potential well turns into a tri-stable one and the potential barrier is reduced greatly.Then,the dynamic responses of the system subject to harmonic excitation and Gaussian white noise excitation are explored by numerical methods and validated by experiments.Compared with a bi-stable energy harvester,the TEH's bandwidth for inter-well oscillation to occur is extended and shifted to low frequency,and consequently the tri-stable device creates a dense high output voltage and power under the low intensity of stochastic excitation.