Stochastic averaging for nonlinear vibration energy harvesting system

A stochastic averaging technique for the nonlinear vibration energy harvesting system to Gaussian white noise excitation is developed to analytically evaluate the mean-square electric voltage and mean output power. By introducing the generalized harmonic transformation, the influence of the external circuit on the mechanical system is equivalent to a quasi-linear stiffness and a quasi-linear damping with energy-dependent coefficients, and then the equivalent nonlinear system with respect to the mechanical states is completely established. The Itô stochastic differential equation with respect to the mechanical energy of the equivalent nonlinear system is derived through the stochastic averaging technique. Solving the associated Fokker–Plank–Kolmogorov equation yields the stationary probability density of the mechanical states, and then the mean-square electric voltage and mean output power are analytically obtained through the approximate relation between the electric quantity and the mechanical states. The agreements between the analytical results and those from the moment method and from Monte Carlo simulations validate the effectiveness of the proposed technique.     

On the use of discontinuous nonlinear bistable dynamics to increase the responsiveness of energy harvesting devices

There is promise in the use of bistable devices to transduce ambient vibrations into electrical power. However, it is critical to sustain the relatively large amplitude snap-through motion, or interwell motion, to significantly improve the responsiveness of bistable devices as compared to linear resonance-based approaches. This work posits that relatively stiff structural elements can be placed in the vicinity of the equilibria of bistable devices such that the discontinuous change in dynamics will tend to eject an otherwise small amplitude motion into the large amplitude interwell orbit that is to be preferred for energy harvesting applications. The discontinuous nonlinear dynamic equations of motion are derived and a proxy system parametrically studied. These numerical studies demonstrate that discontinuous nonlinear bistable devices have a significantly broadened frequency range that elicits the large amplitude snap through behavior. It is also seen that interwell motion is achievable at significantly reduced excitation amplitudes through these discontinuous structural elements.     

High-energy orbit sliding mode control for nonlinear energy harvesting

Nonlinear Dynamics - This paper is concerned with the chaotic dynamics of a rotating pendulum system with bistable characteristics subjected to a viscous damping and a harmonic forcing. As a...     

Clearance-type nonlinear energy sinks for enhancing performance in electroacoustic wave energy harvesting

This paper explores a clearance-type nonlinear energy sink (NES) for increasing electrical energy harvested from non-stationary mechanical waves, such as those encountered during impact and intermittent events. The key idea is to trap energy in the NES such that it can be harvested over a time period longer than that afforded by the passing disturbance itself. Analytical, computational, and experimental techniques are employed to optimize the energy sink, explore qualitative behavior (to include bifurcations), and verify enhanced performance. Unlike traditionally studied single-DOF NESs, both subdomains of the NES (i.e., on either side of the clearance) contain displaceable degrees of freedom, increasing the complexity of the analytical solution approach. However, closed-form solutions are found which quantify the relationship between the impact amplitude and the energy produced, parameterized by system properties such as the harvester effective resistance, the clearance gap, and the domain mass and stiffness. Bifurcation diagrams and trends therein provide insight into the number and state of impact events at the NES as excitation amplitude increases. Moreover, a closed-form Poincaré map is derived which maps one NES impact location to the next, greatly simplifying the analysis while providing an important tool for follow-on bifurcation studies. Finally, a series of representative experiments are carried out to realize the benefits of using clearance-type nonlinearities to trap wave energy and increase the net harvested energy.     

A nonlinear hybrid energy harvester with high ultralow-frequency energy harvesting performance

Meccanica - The exploration of renewable energy technology is increasingly important owing to depletion of fossil fuels and the environmental pollution caused by the use of fossil fuels. Converting...     

On the efficiency of energy harvesting using vortex-induced vibrations of cables

Many technologies based on fluid–structure interaction mechanisms are being developed to harvest energy from geophysical flows. The velocity of such flows is low, and so is their energy density. Large systems are therefore required to extract a significant amount of energy. The question of the efficiency of energy harvesting using vortex-induced vibrations (VIV) of cables is addressed in this paper, through two reference configurations: (i) a long tensioned cable with periodically-distributed harvesters and (ii) a hanging cable with a single harvester at its upper extremity. After validation against either direct numerical simulations or experiments, an appropriate reduced-order wake-oscillator model is used to perform parametric studies of the impact of the harvesting parameters on the efficiency. For both configurations, an optimal set of parameters is identified and it is shown that the maximum efficiency is close to the value reached with an elastically-mounted rigid cylinder. The variability of the efficiency is studied in light of the fundamental properties of each configuration, i.e. body flexibility and gravity-induced spatial variation of the tension. In the periodically-distributed harvester configuration, it is found that the standing-wave nature of the vibration and structural mode selection plays a central role in energy extraction. In contrast, the efficiency of the hanging cable is essentially driven by the occurrence of traveling wave vibrations.     

On the dynamics around targeted energy transfer for vibro-impact nonlinear energy sink

A periodically forced linear oscillator with impact attachment has been studied. An asymptotical analytical method has been developed to obtain the fixed points and to analyze the transient 1:1 resonance (two impacts per cycle) of the modulated response. The influence of parameters on dynamics has been analyzed around the slow invariant manifold (SIM). Five different response regimes have been observed from theoretical and numerical results. It is demonstrated that they are closely related to the topological structure and relative position of fixed points. The bifurcation, route to chaos and the efficiency of targeted energy transfer (TET) with the variation of different parameters (i.e., amplitude and frequency of excitation, clearance, damping, mass ratio and restitution coefficient) have been investigated and well explained around SIM. Experimental results validate the existence of different regimes and different routes to chaos by the variation of the return map of time difference between consecutive impact moments. TET phenomenon has been analyzed for a strongly modulated response, and different cases of TET have been observed and analyzed. It is clearly observed that TET depends not only on whether there exists 1:1 resonance, but also on impulse strength during the transient resonance capture.     

Dynamics of an electromagnetic vibro-impact nonlinear energy sink,applications in energy harvesting and vibration absorption

Nonlinear Dynamics - The dynamics of an electromagnetic vibro-impact nonlinear energy sink (VINES) is investigated. The system consists of a linear oscillator equipped with multiple turns of coil,...     

Mechanically and electrically nonlinear non-ideal piezoelectric energy harvesting framework with experimental validations

Nonlinear Dynamics - In the literature of vibration energy harvesting, mechanically nonlinear frameworks have mostly employed linear electrical circuitry to formulate AC input–AC output...     

Vibration energy harvesting from impulsive excitations via a bistable nonlinear attachment

A vibration-based bistable electromagnetic energy harvester coupled to a directly excited primary system is examined numerically. The primary goal of the study is to investigate the potential benefit of the bistable element for harvesting broadband and low-amplitude vibration energy. The considered system consists of a grounded, weakly damped, linear oscillator (LO) coupled to a light-weight, weakly damped oscillator by means of an element which provides both cubic nonlinear and negative linear stiffness components and electromechanical coupling elements. Single and repeated impulses with varying amplitude applied to the LO are the vibration energy sources considered. A thorough sensitivity analysis of the system's key parameters provides design insights for a bistable nonlinear energy harvesting (BNEH) device able to achieve robust harvesting efficiency. This is achieved through the exploitation of three BNEH main dynamical regimes; namely, periodic cross-well, aperiodic (chaotic) cross-well, and in-well oscillations.     

Energy harvesting in a nonlinear energy sink absorber using delayed resonators

Nonlinear Dynamics - This paper examines periodic and quasi-periodic (QP) vibration-based energy harvesting (EH) in a nonlinear energy sink (NES) absorber that is coupled to an electric circuit...     

A review of nonlinear piezoelectric energy harvesting interface circuits in discrete components

Piezoelectric energy harvesting is considered as an ideal power resource for low-power consumption gadgets in vibrational environments. The energy extraction efficiency depends highly on the interface circuit, and should be highly improved to meet the power requirements. The nonlinear interface circuits in discrete components have been extensively explored and developed with the advantages of easy implementation, stable operation, high efficiency, and low cost. This paper reviews the state-of-the-art progress of nonlinear piezoelectric energy harvesting interface circuits in discrete components. First, the working principles and the advantages/disadvantages of four classical interface circuits are described. Then, the improved circuits based on the four typical circuits and other types of circuits are introduced in detail, and the advantages/disadvantages, output power, efficiency, energy consumption, and practicability of these circuits are analyzed. Finally, the future development trends of nonlinear piezoelectric energy harvesting circuits, e.g., self-powered extraction, low-power consumption, and broadband characteristic, are predicted.

     

Relationship between multibody dynamics computation and nonlinear vibration theory

This paper presents the ground-work of implementing the multibody dynamics codes to analyzing nonlinear coupled oscillators. The recent developments of the multibody dynamics have resulted in several computer codes that can handle large systems of differential and algebraic equations (DAE). However, these codes cannot be used in their current format without appropriate modifications. According to multibody dynamics theory, the differential equations of motion are linear in the acceleration, and the constraints are appended into the equations of motion through Lagrange's multipliers. This formulation should be able to predict the nonlinear phenomena established by the nonlinear vibration theory. This can be achieved only if the constraint algebraic equations are modified to include all the system kinematic nonlinearities. This modification is accomplished by considering secondary nonlinear displacements which are ignored in all current codes. The resulting set of DAE are solved by the Gear stiff integrator. The study also introduced the concept of constrained flexibility and uses an instantaneous energy checking function to improve integration accuracy in the numerical scheme. The general energy balance is a single scalar equation containing all the energy component contributions. The DAE solution is then compared with the solution predicted by the nonlinear vibration theory. It also establishes new foundation for the use of multibody dynamics codes in nonlinear vibration problems. It is found that the simulation CPU time is much longer than the simulation of the original equations of the system.     

Integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frames

This paper establishes the integral theory for the dynamics of nonlinearnonholonomic system in noninertial reference frame.Firstly,based on the Routhequation of the relative motion of nonlinear nonholonomic system gives the firstintegral of the system.Secondly,by using cyclic integral or energy integral reduces theorder of the equation and obtains generalized Routh equation and Whittaker equationrespectively.Thirdly,derives canonical equation and variation equation and by usingthe first integral constructs integral invariant.And then,establishes the basic integralvariants and the integral invariant of Poincare-Cartan type.Finally,we give a series ofdeductions.     

复杂非线性系统的某些动力学理论与应用

自然界和工程技术中存在大量的非线性因素和现象,非线性动力学奠定了研究非线性系统丰富多样的运动模式和演化过程的定性或定量规律的坚实理论基础．非线性动力学的研究深刻地揭示了客观世界的复杂性和多样性,它不仅对数理科学的发展有重大理论意义,而且与其他学科广泛交叉,在各个科学技术领域都有十分广阔的应用前景．     

On problems in the weakly nonlinear theory of hydrodynamic stability and its improvement

There are three main problems in the weakly nonlinear theory of hydrodynamic stability: (1)The radius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it. (2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems. (3)When the linear part of its solution does not correspond to a neutral case, there are more than one way in determining the Landau constants, and practically no one knows which is the best way. In this paper, problems(1) and (2)are solved theoretically, and ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clarified. Project supported by the National Natural Science Foundation of China