Study On Nonlinear Dynamics Behavior And Application Of Multi-stable Energy Harvesting Systems

The design of a new type of vibration structure is an indispensable link in the development of energy harvesting technology.Traditional linear vibration devices have high power generation efficiency only when the vibration frequency of external excitation source is close to its natural frequency;the nonlinear devices based on magnetoelastic structure have the technical problems of magnetic coupling and single electromechanical conduction mechanism.Although there are some multi-stable spring-mass systems in engineering,the application of multi-stable spring-mass systems in the field of vibration energy harvesting is restricted due to the lack of theoretical research on multi-stable dynamics,unclear response mechanism and imperfect research methods.In this paper,based on the multi-stable spring-mass system derived from smooth and discontinuous(SD)oscillators,the electromechanical coupling dynamic model of energy harvesting system is established,the nonlinear characteristics of multi-stable vibration energy harvesting system are studied,its complex dynamic behavior and response mechanism are clarified,and the theoretical framework of multi-stable dynamics is enriched.The multi-stable springmass system is a new method for vibration energy harvesting,which avoids the magnetic coupling interference caused by the design of magnetoelastic structures,and provides a new method for engineering application problems such as wide-band weak excitation intensity and vibration energy harvesting under low-or ultra-low-frequency excitation.The main research contents and results are as follows:New types of electromagnetic and electromagnetic-piezoelectric hybrid bistable vibration energy harvesting systems are designed,and the electromechanical coupling control equation of the system is obtained.The electromechanical coupling control equation is decoupled by generalized harmonic transformation,and the equivalent nonlinear control equation is obtained.Firstly,the response statistical characteristics of electromagnetic bistable vibration energy harvesting system under the excitation of Gaussian white noise are studied by using stochastic averaging method.The effects of system parameters on the steady-state probability density,average harvested power and stochastic resonance are discussed.Under the condition of stochastic resonance,the system can generate large amplitude vibration,thus improving the performance of energy harvesting.Secondly,an electromagnetic-piezoelectric hybrid bistable vibration energy harvesting system is de-signed.The effective potential energy,stochastic P-bifurcation,average harvested power and the stability of periodic attractors under the excitation of Gaussian colored noise are analyzed.It is found that noise-enhanced stability occurs during the transition from largeamplitude periodic attractor to small-amplitude periodic attractor,which indicates that the stability of large-amplitude periodic attractor can be enhanced by noise excitation.The average lifetime of the periodic attractor is longer than the deterministic decay time,which is very useful for energy harvesting.The effects of time-delayed feedback signals on the dynamics and performance of a hybrid vibration energy harvesting system with different types of excitations are studied,and its electromechanical equations are derived and solved.In this study,the broadband energy harvesting characteristics under harmonic excitation and the steady-state response characteristics under stochastic excitation are taken as optimization criteria,which provide guidance for the design of time-delayed feedback signal parameters and the optimization of different types of external excitation.The purpose is to improve the performance of the bistable hybrid vibration energy harvesting system.It is found that the time-delayed feedback signal can stabilize the unstable periodic orbit of the attractor,increase the maximum total average harvested power of the system and enhance the stochastic resonance phenomenon.By comparing the harvesting performance under different time-delayed feedback signals,it is concluded that the time-delayed energy harvester has superior characteristics over other design schemes.An electromagnetic-piezoelectric hybrid tri-stable vibration energy harvesting system is established.By adjusting geometric parameters,it is found that the system has different nonlinear stiffness characteristics of hardening spring effect,softening spring effect and hardening-softening spring effect.The extended average method and FokkerPlanck-Kolmogorov equation analysis method are developed for the electromechanical coupling control equation of vibration energy harvesting system.Through dynamic analysis and performance evaluation of the system under harmonic and stochastic excitation,it is found that the effective frequency bandwidth of the energy amplification region and resonance band can be easily adjusted to meet different working conditions such as ultralow frequency and ultra-low excitation intensity.Two simple general structures are proposed to realize different types of quad-stable vibration energy harvesting systems by adjusting the geometric parameters of linear springs.The energy generation and dynamic behavior of the system under stochastic and harmonicexcitation sources are analyzed by using the Fokker-Planck-Kolmogorov equation analysis and extended averaging method.Under stochastic excitation,with the increase of noise intensity in the quad-stable system,the mean square value of displacement and the average harvested power first decrease,then increase slightly.The expected values of mean square value of displacement and average harvested power increase with the increase of system steady state from bistable to quad-stable state.Under harmonic excitation,the quad-stable system can realize high-energy inter-well motion with large amplitude periodic oscillation,thus significantly increasing the response of relative displacement,velocity and harvested current.Even at relatively weak excitation intensity or frequency,the quad-stable vibration energy harvesting system can achieve fast large amplitude vibration throughout all steady-state,and enhance the performance of energy harvesting.A multi-directional multi-stable system of linkage-spring-mass is established,whose steady-state number and steady-state position are adjustable,so as to adjust the effective frequency bandwidth of the energy amplification interval and the resonance frequency band to meet different working environments.The multi-directional multi-stable system produces a large amplitude response at ultra-low frequencies,enabling motion throughout all equilibrium positions of ultra-low frequency vibration sources.Dynamic simulation and experimental results verify the correctness of the theoretical analysis.Based on energy harvesting technology,an intelligent vibration isolation system of self-powered time-delayed isolator is constructed,which is composed of multi-stable vibration energy harvester,quasi-zero-stiffness isolator and time-delayed feedback controller.The dynamics and performance of self-powered time-delayed quasi-zero-stiffness isolator are studied,and the vibration isolation mechanism of self-powered time-delayed isolator is expounded.The analysis of vibration isolation performance shows that the increase of time-delayed feedback control can further broaden the bandwidth of quasizero-stiffness isolator,improve the isolation performance of low frequency band,and effectively suppress the peak value of primary resonance.The self-powered time-delayed isolator has strong feasibility and superior performance,and has the characteristics of time-delayed feedback control and low frequency vibration isolation.