Nonlinear Vibration Energy Harvester Research Articles

Physical realisation of a nonlinear electromagnetic energy harvester for rotational applications

Control and structural health monitoring sensors are becoming increasingly common in industrial and household applications due to recent advances reducing their manufacturing costs, size and power consumption. Nevertheless, providing power for these sensors poses a key challenge to engineers, particularly in system locations where limited access renders regular maintenance infeasible due to high associated costs. In the present work, the design and physical prototype testing of a nonlinear electromagnetic vibration energy harvester is presented based on a previously reported concept of the authors. The harvester is activated by the torsional speed fluctuations of a rotating shaft. Experimental testing in a rig driven by an electric motor confirms the harvester’s properties and the modelled oscillatory behaviour. This novel rotational vibration energy harvester concept may generate over 10 mW of electrical power for a broadband speed range of approximately 400 rpm (in the examined rotational system with set fluctuating speed) for wireless sensing purposes on rotating shafts.

Multiple electrically tunable parametric resonances in a capacitively coupled electromechanical resonator for broadband energy harvesting

Parametric excitation (PE) has widely been employed as a method of mechanical pre-amplification in nonlinear vibration energy harvesting systems. However, despite their advantages, most current PE systems are limited to degenerate parametric operation within a narrow frequency band around the primary instability tongue. In this paper, we simulate and experimentally demonstrate a parametrically driven capacitive electromechanical resonator having multiple electrical degrees of freedom. Multiple modes allow for several frequency bands in which the electrical resonator is driven into nondegenerate (combination) parametric resonance (PR) in addition to degenerate resonance, thereby enabling operation over a broader range of frequencies while maintaining the same mechanical footprint. These frequency bands and PR thresholds are tunable by simply changing the electrical circuit parameters and PR can be achieved in the presence of high mechanical damping making the method more adaptable than purely mechanical approaches. Experimental results are extended by simulations indicating that proper selection of operating parameters can enable the merging of instability tongues to produce a broadband region of PR for elastic wave energy harvesting thereby obtaining superior performance when compared to an equivalent single degree of freedom PE energy harvester.

Enhancement of the performance of nonlinear vibration energy harvesters by exploiting secondary resonances in multi-frequency excitations

This study is concerned with utilizing secondary resonances in order to harvest energy from low-frequency excitations. Nonlinearities give rise to secondary resonances, which can potentially activate large-amplitude responses when the excitation frequency is a fraction of the fundamental frequency of the system. Such resonances offer an untapped and unique opportunity for harvesting vibratory energy from excitation sources with low-frequency components. This issue has propelled the current study. Based on multi-frequency excitation, we develop a novel theoretical framework for a piezomagnetoelastic energy harvester to enhance its performance. The proposed scheme is implemented in both monostable and bistable piezomagnetoelastic under low-frequency excitations. It is shown throughout the paper that when the excitation frequencies are certain fractions of the system's fundamental frequency, the combination and simultaneous resonance activate large-amplitude responses. Another advantage of the scheme is that the energy could be harvested from low-frequency ambient vibrations, which is a considerable concern in this field of study. Different responses of the system, such as low-amplitude and high-amplitude limit-cycle oscillations and chaotic motions, are studied through perturbation theory and numerical techniques. Various numerical tools, including phase portrait, Poincare section, and Lyapunov exponent, are used to explore complex dynamical behavior of the system. The performance of the harvester is also compared in different regions. Numeral simulations clearly confirm that the proposed framework dramatically enhances the performance of the energy harvester.

On the Optimization of a Multimodal Electromagnetic Vibration Energy Harvester Using Mode Localization and Nonlinear Dynamics

In this paper we study a generic model of a nonlinear quasiperiodic vibration energy harvester (VEH) based on electromagnetic transduction. The proposed device consists of multiple moving magnets guided by elastic beams and coupled by repulsive magnetic forces. A system of two degrees-of-freedom (DOFs) with tunable nonlinearity and mode localization is experimentally validated. The validated 2-DOFs harvester is optimized using a multiobjective optimization procedure to improve its harvested power and frequency bandwidth. An efficient criterion using the modal kinetic energy of the finite element model is proposed to quantify the energy localized in the structure perturbed zones. Afterward, this concept has been generalized to a 5-DOFs VEH with two perturbed DOFs oscillators and the optimal performances are derived using a multiobjective optimization. This proposed model enables a significant increase in the harvested power and frequency bandwidth by 101% and 79%, respectively, compared to that of the 2-DOFs device. Moreover, it has been shown that harvesting energy from two perturbed magnets among five provides almost the same amount of harvested energy and enhances the frequency bandwidth by 18% compared to those of the periodic system. Consequently, the harvester can be improved by reducing the transduction circuits number and the manufacturing cost.

A wind-induced negative damping method to achieve high-energy orbit of a nonlinear vibration energy harvester

Maintaining high-energy orbit oscillation of a nonlinear vibration energy harvester (VEH) is the key to achieve high-performance, broadband energy harvesting. Conventional orbit-jump strategies, such as mechanical modulation or electrical control methods, need to consume the limited harvested energy and may unfavourably reduce the energy harvesting efficiency. To avoid the undesired energy consumption, we focus on utilizing the overlooked wind energy to assist a nonlinear VEH to attain the preferred high-energy orbit. The novel orbit-jump method proposed in this letter is based on the wind-induced negative damping mechanism and the resultant self-excited behaviour. Both numerical simulation and experimental results validate the feasibility of the proposed method to efficiently trigger the high-energy orbit oscillations of a nonlinear VEH. Moreover, the required wind energy to achieve self-excited oscillation for different excitation frequencies and acceleration levels, is quite stable and can be easily satisfied, which demonstrates good robustness for practical applications.

Bifurcation Analysis of a Bistable Nonlinear Vibration Energy Harvester with Elastic Boundary

This paper presents a novel bistable vibration energy harvester with an elastic boundary (BVEH_EB). The bistable nonlinearity of the BVEH_EB is realized by an inclined spring, which could induce a large-amplitude inter-well response to pursue high harvesting efficiency. The elastic boundary brings additional dynamic coupling with the inclined spring to reduce the depth of the potential energy well, which could enhance the inter-well response. The bifurcation responses in terms of different parameters such as the magnet mass, the inclined spring stiffness, the excitation frequency, and the excitation amplitude are numerically investigated. Abundant nonlinear phenomena, such as intra-well oscillation, inter-well oscillation, chaos, etc., are observed. The design guidelines of the BVEH_EB are developed, which could provide a novel harvesting method.

Tapered nonlinear vibration energy harvester for powering Internet of Things

The lack of a sustainable power source to substitute batteries for long-term applications limits the widespread deployment of wireless sensor nodes in this era of the Internet of Things. Conventional linear Vibration Energy Harvesters are inefficient in converting ambient mechanical energy into usable electrical energy owing to their narrow frequency bandwidth when harnessing mechanical energy that is spread over a wide range of frequencies. In this work, we design, develop and demonstrate high power density nonlinear wideband energy harvesters using novel tapered spring architectures in an autonomous wireless sensor node system. These spring structures exhibit a nonlinear restoring force arising from the atypical stress distribution that can be additionally tuned by changing the taper-ratio in the structure. We investigate different tapering designs in order to achieve optimal spring hardening nonlinearities. This nonlinearity aids in widening the operable bandwidth, making the harvesters suitable for scavenging energy from real-world broadband vibrations. We obtain power densities of the order of 2660 μW/cm3g2 in the nonlinear energy harvester, outpacing most contemporary energy scavengers. We present a modified Perturb and Observe algorithm that allows tracing of the maximum power point in the context of non-stationary vibration conditions. We use the fabricated nonlinear device to power a wireless sensor node that reports on vital physical parameters (humidity, temperature), thereby enabling a resilient remote data acquisition system. This demonstrates the potential of our design to provide a sustainable energy source for platforms within the Internet of Things.

Piezoelectric passive self-tuning energy harvester based on a beam-slider structure

This paper investigates a passive self-tuning piezoelectric energy harvester based on a beam-slider structure. The hardening nonlinearity is imparted to the system by two repulsive magnets to achieve broad bandwidth. The slider on the slightly tilted cantilever beam can automatically move along the beam to destabilize the low-energy orbit and track the high-energy orbit. The results of simulation and experiments show that the proposed design enables the nonlinear energy harvester to acquire a high energy converting efficiency and possess the anti-interference ability. In the frequency range of 21Hz-23Hz, the output power is enhanced by more than 25 times over the case with fixed mass at the free end. The tuning process is completely passive without any active actuators or sensors, which provides a promising method for designing an efficient nonlinear vibration energy harvester.

Analysis of the component forces of the nonlinear magnetic force in energy harvester

In the piezoelectric vibration energy harvester, permanent magnets are often used to generate nonlinear applied magnetics force to improve the energy utilization rate of the system, the modeling analysis and accurate calculation of the force between magnets in the system is a difficult problem in the study of nonlinear bistable vibration energy harvesting. During the deformation of the cantilever beam, the direct force of the permanent magnet block can be divided into horizontal and vertical component forces. In most existing literatures analyzing such problems, the magnetizing current method magnetic force calculation model of double-stabilized electric beam mainly considers the influence of vertical magnetic force on the system of cantilever beam, and it is considered that the horizontal component of magnetic force has little influence on the vibration response of cantilever beam, but there is no detailed proof and elaboration of this problem. In this paper, the magnetic force, the effect of magnetic force on natural frequency and magnetic potential energy are calculated and simulated from three aspects. Through the comparison of results, it is proved that the effect of the horizontal magnetic force on the whole nonlinear piezoelectric beam vibration energy harvester can be ignored.

Disturbance observer–based terminal sliding mode control for effective performance of a nonlinear vibration energy harvester

We propose a new scheme to control the coexisting attractors in a bistable piezomagnetoelastic power generator. Coexisting periodic or chaotic attractors frequently occur in nonlinear energy harvesters. For effective performance of the energy harvester, the system is desired to operate on the high-energy periodic orbit. Therefore, a controller may be used to force the system to operate on the high-energy orbit. In the present research, a disturbance observer–based terminal sliding mode control with input saturation is proposed to push the system from low-energy periodic and chaotic attractors to high-energy periodic attractors. Furthermore, to minimize the energy required for the controller, a genetic algorithm optimization is employed to determine the bound of the input saturation and parameters of the controller. A major advantage of the proposed control technique is tracking control while control input limitations, significant concerns for energy harvesting purpose, are present. The Lyapunov stability theorem of the closed-loop system is proven in the presence of control input saturation and external disturbance. In addition to the primary resonance, superharmonic resonance is considered. The numerical results show that the proposed method can successfully control and shift the vibration energy harvesting system between different attractors in the presence of uncertainty and with minimal control energy budget.

Characterization of challenges in asymmetric nonlinear vibration energy harvesters subjected to realistic excitation

With an explosion of the internet of things (IoT), vibration energy harvesting provides an environmentally friendly solution to replace consumable batteries in powering IoT wireless sensors. Yet, when implemented in practice, ambient vibration input energy is much less periodic than assumptions adopted in previous studies. This becomes especially important given that asymmetries are inevitable in nonlinear device platforms. This research sheds light on these complex challenges of practical vibration energy harvesting by developing and exploring an analytical model based on equivalent linearization. The modeling approach provides an opportunity to understand influences of asymmetry, nonlinearity, and combined excitation response on the DC power delivery of energy harvesters. In the analytical model, a weighted Gaussian joint distribution is utilized to approximate the influences caused by the random excitation. Combined with numerical and experimental validation, the analysis indicates that with the increase of stochastic base acceleration, two outcomes are possible. A first outcome involves an enhancement of DC power by way of triggering large amplitude nonlinear oscillations. A second outcome corresponds to a loss of high power delivery since the noise interferes with the attainment of the snap-through dynamic. Either reducing asymmetry or increasing harmonic excitation component is found to be favorable to induce the power-enhancing dynamics and inhibit the occurrence of the second case. Although with the simplified Gaussian distribution, the analytical framework cannot reproduce exact details of the dynamic responses in every case, the results show that the statistical trends of the analysis are overall borne out in simulation and experiment. This indicates the new modeling of this research may help guide attention to design and deployment techniques for nonlinear vibration energy harvesters in practical combined excitation environments, where limitations on precise manufacture or placement may introduce structural asymmetry.

Review of nonlinear vibration energy harvesting: Duffing, bistability, parametric, stochastic and others

Vibration energy harvesting typically involves a mechanical oscillatory mechanism to accumulate ambient kinetic energy, prior to the conversion to electrical energy through a transducer. The convention is to use a simple linear mass-spring-damper oscillator with its resonant frequency tuned towards that of the vibration source. In the past decade, there has been a rapid expansion in research of vibration energy harvesting into various nonlinear vibration principles such as Duffing nonlinearity, bistability, parametric oscillators, stochastic oscillators and other nonlinear mechanisms. The intended objectives for using nonlinearity include broadening of frequency bandwidth, enhancement of power amplitude and improvement in responsiveness to non-sinusoidal noisy excitations. However, nonlinear vibration energy harvesting also comes with its own challenges and some of the research pursuits have been less than fruitful. Previous reviews in the literature have either focussed on bandwidth enhancement strategies or converged on select few nonlinear mechanisms. This article reviews eight major types of nonlinear vibration energy harvesting reported over the past decade, covering underlying principles, advantages and disadvantages, and application-specific guidance for researchers and designers.

Energy and Phase Space Analysis of Response Stabilization Control for Nonlinear Wideband Vibration Energy Harvesting

Energy and Phase Space Analysis of Response Stabilization Control for Nonlinear Wideband Vibration Energy Harvesting

Nonlinear resonance-type electromagnetic vibration energy harvester excited by an impact ball

Nonlinear resonance-type electromagnetic vibration energy harvester excited by an impact ball

Analysis of nonlinear vibration energy harvesters using a complex dynamic frequency method

To understand the complicated dynamic behavior of a Nonlinear Piezoelectric Energy Harvester (NPEH), this paper develops an improved Complex Dynamic Frequency (CDF) method based on complex normal form. CDF introduces a dynamic frequency factor and establishes a set of algebraic equations in handling the effect of higher-order nonlinear terms in a wide frequency band to obtain periodic responses of NPEH. Numerical and experimental studies verify that the proposed CDF gives consistent and accurate predictions of the systems with both weak and strong nonlinearity. Furthermore, through an implicit relationship between magnet arrangement and output performance, one may effectively control the sweep frequency with softening and hardening characteristics. That is a major breakthrough toward the further nonlinear design for broad bandwidth harvesters. As the application, the experimental results reveal the high response profiles can be in a wide frequency range from 10.8 Hz to 24.5 Hz for the NPEH developed that allows an output power of 9 times higher than the conventional linear structure.

A Nonlinear Energy Harvester Operated in the Stochastic Resonance Regime for Signal Detection/Measurement Applications

An energy harvester can operate as a sensor. This article investigates the behavior of a snap-through buckling beam, which underpins a nonlinear vibrational energy harvester (NLEH), in the presence of noisy vibrations superimposed on a subthreshold deterministic input signal. In particular, we concentrate on a specific operating regime, in which noise-mediated cooperative behavior, specifically “stochastic resonance” (SR), can be exploited in signal detection scenarios. We consider a sinusoidal signal with amplitude below the switching threshold of the NLEH, i.e., the signal alone does not lead to switching between the stable states of the NLEH. As expected, there exists an optimal noise intensity at which the response signal-to-noise ratio (SNR) passes through a maximum, the hallmark of the SR effect. The harvesting performance, quantified by the generated electrical power and the mechanical-electrical conversion efficiency, is examined as a function of the amplitude/frequency of the deterministic signal, and the noise intensity. Realizing that both the SR effect and the most efficient energy-harvesting (EH) behavior depend on the rate of switching events across the energy barrier of the device, we find that “tuning” to the SR regime does, in fact, improve signal detection, as should be expected. However, the EH performance improves with larger noise values. Therefore, the regimes for optimal signal detection and highest electrical power generation are different, with increasing noise intensity yielding better EH performance. There does exist, however, the intriguing possibility that, by carefully configuring the electrical stage of the NLEH, one could realize an autonomous sensor that collects electrical power to charge a capacitor and utilizes it to power the electronics for signal detection/analysis in the SR regime.

Response analysis of the nonlinear vibration energy harvester with an uncertain parameter

In this paper, the Chebyshev polynomial approximation is firstly utilized to analyze the dynamical characteristics of the nonlinear vibration energy harvester with an uncertain parameter. First, the stochastic energy harvester is transformed into a high-dimensional equivalent deterministic system by the Chebyshev polynomial approximation. And the ensemble mean response of the stochastic energy harvester is introduced to discuss the stochastic response. Then, the effectiveness of the approximation method is verified by numerical results. Furthermore, the bifurcation property of the displacement and voltage is analyzed, which is also consistent with the results derived by the top Lyapunov exponent. It is found that random factor can induce the appearance of multi-periodic phenomena and lead to appear the behavior of the periodic bifurcation. The strong random factor induces the fluctuation of the output voltage. In addition, the existence of the random factor greatly influences the property of the sub-harmonics and super-harmonics of the spectrum. Overall, the response mechanism of the nonlinear vibration energy harvester with an uncertain parameter is revealed.

Toward self-powered nonlinear wideband vibration energy harvesting with high-energy response stabilization

This paper describes an effort to develop a nonlinear wideband vibration energy harvester with self-powered stabilization control of its high-energy response. In a Duffing-type nonlinear wideband energy harvester, a well-recognized difficulty of coexisting attractors arises so that the emergence of the response in the high-energy branch is not guaranteed because it depends on the initial conditions to which steady-state solutions the state is attracted. The response stabilization control technique introduces a negative resistance which returns the harvested power to the nonlinear resonator to destabilize the undesirable low-energy solution and make the high-energy solution globally stable. In this paper, the power balance of the response stabilization control under intermittent disturbances is first experimentally studied, and a charging circuit to self-power the negative impedance converter (NIC) in the control circuit is then developed. It is concluded that the energy consumed by the NIC can be retrieved by the energy harvesting in 100 seconds even in the worst case.

Harmonic analysis and experimental validation of bistable vibration energy harvesters interfaced with rectifying electrical circuits

The high-performing, nonlinear vibration energy harvesters are conventionally investigated when integrated with simplified resistive electrical circuits (AC circuits), while in fact DC voltages are needed for electronics and rechargeable batteries in practical applications. To lead to an accurate and effective set of design guidelines for realistic energy harvesting system development, an analytical, harmonic balance based method is proposed to characterize the steady state performance and investigate the DC circuit effects. During the route of the analysis method, the induced nonlinear, piecewise piezovoltage is firstly approximated via smooth dynamic responses based on the energy equivalence, which enables the followed harmonic balance operation to analytically estimate the vibration amplitude. The parameter studies show the pros and cons of the coupling constant and resistive load. In one side, with increasing the coupling constant or load resistance during their moderate range, higher electric power is extracted. In the other side, higher piezoelectric coupling and resistive load compromise the beneficial bandwidth of snap-through vibrations. Moreover, comparisons are conducted to reveal the different structural roles of the standard electrical circuit and AC circuit. It is found that AC circuit exhibits equivalent damping effect while the standard rectifying electrical circuit exhibits both equivalent damping and stiffness effects to the harvester system. These different circuit effects explain the theoretically predicted and numerically validated phenomena that the standard rectifying electrical circuit extracts less electric power than AC circuit under moderate piezoelectric coupling constants and resistive loads, while outperforms AC circuit when the coupling constants or load resistances are relatively large.

A Nonlinear Broadband Electromagnetic Vibration Energy Harvester Based on Double-Clamped Beam

The performance of vibration energy harvesters is usually restricted by their frequency bandwidth. The double-clamped beam with strong natural nonlinearity is a simple way that can effectively expand the frequency bandwidth of the vibration energy harvester. In this article, a nonlinear electromagnetic vibration energy harvester with monostable double-clamped beam was proposed. A systematic analysis was conducted and a distributed parameter analytical model was established. On this basis, the output performance was estimated by the analytical model. It was found that the nonlinearity of the double-clamped beam had little influence on the maximum output, while broadening the frequency bandwidth. In addition, the resonant frequency, the frequency bandwidth, and the maximum output all increased following the increase of excitation level. Furthermore, the resonant frequency varies with the load changes, due to the electromagnetic damping, so the maximum output power should be gained at its optimum load and frequency. To experimentally verify the established analytical model, an electromagnetic vibration energy harvester demonstrator was built. The prediction by the analytical model was confirmed by the experiment. As a result, the open-circuit voltage, the average power and the frequency bandwidth of the electromagnetic vibration energy harvester can reach up to 3.6 V, 1.78 mW, and 11 Hz, respectively, under only 1 G acceleration, which shows a prospect for the application of the electromagnetic vibration energy harvester based on a double-clamped beam.