On the dynamics of a nonlinear energy harvester with multiple resonant zones

Nonlinear Dynamics - The dynamics of a nonlinear vibration energy harvester for rotating systems is investigated analytically through harmonic balance, as well as by numerical analysis. The...     

Integration of a nonlinear energy sink and a piezoelectric energy harvester

A mechanical-piezoelectric system is explored to reduce vibration and to harvest energy. The system consists of a piezoelectric device and a nonlinear energy sink(NES), which is a nonlinear oscillator without linear stiffness. The NES-piezoelectric system is attached to a 2-degree-of-freedom primary system subjected to a shock load. This mechanical-piezoelectric system is investigated based on the concepts of the percentages of energy transition and energy transition measure. The strong target energy transfer occurs for some certain transient excitation amplitude and NES nonlinear stiffness. The plots of wavelet transforms are used to indicate that the nonlinear beats initiate energy transitions between the NES-piezoelectric system and the primary system in the transient vibration, and a 1:1 transient resonance capture occurs between two subsystems.The investigation demonstrates that the integrated NES-piezoelectric mechanism can reduce vibration and harvest some vibration energy.     

Bayesian system identification and chaotic prediction from data for stochastic Mathieu-van der Pol-Duffing energy harvester

In this paper, the approximate Bayesian computation combines the particle swarm optimization and sequential Monte Carlo methods, which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system. Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed, which verifies the effectiveness of the proposed method. Finally, a partial response sample of the regular and chaotic responses, determined by the maximum Lyapunov exponent, is applied to detect whether chaotic motion occurs in them by a 0–1 test. This paper can provide a reference for data-based parameter identification and chaotic prediction of chaotic vibration energy harvester systems.     

On the design of an electromagnetic aeroelastic energy harvester from nonlinear flutter

A new energy harvester by coupling the electromagnetic induction and the pitch vibration of a rigid wing is built up in this paper. It is aimed: (1) to harvest energy from the pitch limit cycle oscillation (LCO) of the wing due to the preloaded free-play nonlinearity; (2) to introduce a theoretical analysis scheme based on the equivalent linearized method into the design of this harvester. With the equivalent linearized method, the domains of the single stable LCO and double stable LCOs are respectively obtained. Combining the analytical and numerical solutions, the single stable LCO along with the stable limit cycle amplitude greater than its corresponding unstable one is recognized as the better mode for harvesting, since the larger limit cycle domain is induced and the more energy are yielded. Based on such chosen mode, analyses of varying parameters are conducted with respect to the plunge stiffness, pitch stiffness, distance of elastic axis from center of gravity, distance of geometric center from elastic axis, load resistance and magnetic flux density. Meanwhile, three indicators are applied to reveal their effects on the harvesting performances: (1) the size of limit cycle domain, (2) the onset velocity of LCO, and (3) the energy output.     

Effects of springs on a pendulum electromechanical energy harvester

This paper studies a model of energy harvester that consists of an electromechanical pendulum system subjected to nonlinear springs. The output power is analyzed in terms of the intrinsic parameters of the device leading to optimal parameters for energy harvesting. It is found that in an appropriate range of the springs constant, the power attains higher values as compared to the case without springs. The dynamical behavior of the device shows transition to chaos.     

Modelling and analysis of a single gimbal gyroscopic energy harvester

This work investigates the non-linear dynamics of a single gimbal gyroscopic energy harvester, excited by a harmonic moment about 1 and 2 axes simultaneously. The governing equations of motion are derived and a numerical model is developed to analyse the forced system response in all three rotational degrees of freedom. Simulations showing the effect of the harmonic forcing frequency and the gyroscopic damping are presented. The results identify the characteristic motion responses and available power of a single gimbal gyroscopic energy harvester including the development of the non-linear responses.     

Stochastic analysis of a nonlinear energy harvester with fractional derivative damping

Nonlinear Dynamics - A fractionally damped vibration energy harvester excited by the wide-band random noise is investigated theoretically in this paper. Firstly, by introducing the generalized...     

Performance of a flapping foil flow energy harvester in shear flows

Through numerical simulations, we investigate the energy harvesting performance of a heaving/pitching foil in shear flow. With two-dimensional Navier–Stokes simulations, we examined the energy harvesting efficiencies of such a system in linear shear flows and compared the results with those in uniform flows. It is found that in low shear rates, the performance of the system in linear shear flow is slightly higher than that in uniform flow, whereas the energy harvesting efficiency is greatly diminished if the shear rate is sufficiently high (this effect is more pronounced in higher frequencies). This is attributed to the effects of linear shear on the vorticity generation and the synchronization between fluid forcing and foil motion – when a strong shear flow is introduced the lift force induced by the leading edge vortex that is in phase with the heaving motion of the foil is diminished. Furthermore, by studying the instability of the wake behind the foil, we confirm that the optimal performance of the foil in linear shear flows is associated with the same physical mechanism that controls the performance of the foil in uniform flows, i.e. the excitation of the most unstable modes in the wake when the oscillation frequency of the foil is close to the frequencies of these modes.     

Time delay improves beneficial performance of a novel hybrid energy harvester

Nonlinear Dynamics - The performances of an energy harvester are usually limited. To improve these, the time-delayed feedback control is used in a novel nonlinear hybrid energy harvester for...     

Robust design optimization of a nonlinear monostable energy harvester with uncertainties

Meccanica - Based on the improved interval extension, a robust optimization method for nonlinear monostable energy harvesters with uncertainties is developed. In this method, the 2nd order terms in...     

Stochastic bifurcations in a nonlinear tri-stable energy harvester under colored noise

In this paper, the stochastic bifurcations and the performance analysis of a strongly nonlinear tri-stable energy harvesting system with colored noise are investigated. Using the stochastic averaging method, the averaged Fokker–Plank–Kolmogorov equation and the stationary probability density (SPD) of the amplitude are obtained, respectively. Meanwhile, the Monte Carlo simulations are performed to verify the effectiveness of the theoretical results. D-bifurcation is studied through the largest Lyapunov exponent calculations, which implies the system undergoes D-bifurcation twice with increasing the nonlinear stiffness coefficients. The effects of the nonlinear stiffness coefficients, noise intensity and correlation time on P-bifurcation are discussed by the qualitative changes of the SPD. Moreover, the relationship between D- and P-bifurcation is explored. If the strength of stochastic jump has obvious gap with respect to the two statuses before and after the occurrence of P-bifurcation, the D-bifurcation will happen, too. Finally, the performance and the capability of harvesting energy from ambient random excitation are analyzed.     

Nonlinear structural dynamics of a new sliding-mode triboelectric energy harvester with multistability

A new sliding-mode triboelectric energy harvester in the form of a cantilever beam with a tip mass that is acted upon by both magnetic and friction forces is modelled and simulated. A numerical scheme based on the trapezoidal rule with the second-order backward difference formula (TR-BDF2) method is introduced to solve the combined non-smooth mechanical and stiff electrical system. This is the first study of the structural dynamics of the sliding-mode triboelectric energy harvesting; additionally, a magnetic field that induces multistability is present. A comparison between the coupled and uncoupled electromechanical models suggests that the electrostatic force between the electrodes can be ignored, which makes the uncoupled model preferable in the dynamical analysis. The influence of the non-conservative force (the friction force) on the multistability of the system is investigated. It is found that the distribution of the multistability on the parametric plane changes even when a small amount of friction is involved, and the areas of bistability and tristability shrink while that of the monostability expands. A comparison among these three types of stability reveals the superiority of invoking bistability as it facilitates broadband energy harvesting. The excitation level plays an important role in inducing the snap-through motion (the interwell oscillation) by enabling the crossing of the energy barriers between wells. The increase in the friction shrinks the frequency band of interwell oscillations from high frequencies down to low frequencies on the discrete frequency sweep. An analysis of the basins of attraction finds that at low frequencies the bistable system can undergo only interwell oscillations, while the tristable system can merely experience intrawell oscillations. The basins can intermingle with each other in both bistable and tristable systems. Finally, an increase in the excitation level can break the basins into discrete pieces and/or points.

     

Design of a quad-stable piezoelectric energy harvester capable of programming the coordinates of equilibrium points

In this study, a novel quad-stable energy harvester (QEH) is developed, in which its coordinates of equilibrium points can be user-defined like programming. This programmable feature distinguishes the proposed QEH from all reported magnet-type or buckling-type vibration energy harvesters. It has the advantage that it is easy to develop a high-performance QEH by appropriately programming these coordinate points and customizing a personalized QEH for different vibration environments. The dynamic model is established by the Ritz method and the Lagrange equation. The analytical steady periodic response is obtained by the average method. When the excitation acceleration is 2 m/s², the peak power is 575 μW at 8.5 Hz. Also, the influence of the coordinate arrangement of the equilibrium points on the energy harvesting performance is studied. A formula that can quickly determine the equilibrium point coordinates is given, and the QEH designed according to this formula has superior performance. At last, the performance of the designed QEH is compared with other reported vibration energy harvesters. It shows that the QEH has a high average output power (287 μW), high normalized power density (59.8 μW/cm³/g²), and wide operating frequency range (8.4 Hz) among these harvesters.

     

双稳态电磁式振动能量捕获器超谐波响应研究

超谐波响应是非线性振动系统在较大激励下表现的特性,在某种条件下双稳态振动能量捕获系统的超谐波响应可使系统产生优越的输出功率。本文将质量-非线性弹簧-阻尼系统与双稳态振动能量捕获器相结合,提出了附加非线性振子的双稳态电磁式振动能量捕获器,建立系统的力学模型及控制方程。采用两项式谐波平衡法,获得了双稳态系统在简谐激励下产生大幅运动的基谐波和超谐波响应的解析解,借助数值仿真分析了质量比和调频比对双稳态振动能量捕获器产生大幅运动的影响规律,获得了双稳态系统的结构参数的最佳配置范围,且当外部激励频率处于低频段时,系统发电主要表现为超谐波发电,随着激励频率的增大,振动发电系统主要呈现基谐波发电。上述研究,为双稳态能量捕获装置的理论研究提供了参考。     

Response analysis of the piezoelectric energy harvester under correlated white noise

Nonlinear Dynamics - Energy harvesting of a monostable duffing-type harvester with piezoelectric coupling under correlated multiplicative and additive white noise is investigated in this paper. The...     

Nonlinear characteristic of a circular composite plate energy harvester: experiments and simulations

Conservative chaotic systems are rare, especially autonomous smooth dynamical systems. This paper reports two four-dimensional (4D) autonomous conservative systems. The conservation of these two systems has been verified using the trace of Jacobian matrix, perpetual point theory and Hamiltonian energy theory. Numerical analyses, including phase portrait, Poincaré section, Lyapunov exponent spectrum and bifurcation diagram, verify the existence of the chaotic and quasiperiodic flows. Moreover, a electronic circuit in Multisim is built to demonstrate their chaotic dynamics, whose circuit experimental results agree well with the numerical results.     

The effect of the beam shapes on the doubly-clamped piezoelectric energy harvester

For a piezoelectric energy harvester composed of a doubly-clamped beam with arbitrary width shapes and a proof mass, the influence of beam shapes and electrode arrangements on different electric outputs is analyzed. The output performances of piezoelectric energy harvesters with rectangular shape, concave trapezoidal shape, and concave parabolic shape are compared, and an optimization way is given. The experimental results validate the effectiveness of the methods.     

Performance improvement of the stochastic-resonance-based tri-stable energy harvester under random rotational vibration

In this paper, the stochastic-resonance-based tri-stable energy harvester (TEH) is proposed to enhance harvesting performance under random rotational vibration. An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered. The stationary probability density function (SPDF) of the harvester is obtained by the improved stochastic averaging. Then, with the adiabatic approximation theory, the analytical expression of signal-to-noise ratio (SNR) for the TEH is deduced to characterize stochastic resonance (SR). To enhance direct current (DC) power delivery from a rotational TEH, the influences of system parameters on SR is discussed. The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system. The TEH has higher harvesting performance under the optimal SR. That is, the optimal parameter combinations can induce optimal SR and maximize harvesting performance. Thus, the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.