Bistable Vibration Research Articles

Chaotic responses across the potential barrier of bistable vortex-induced vibration energy harvesters

Large-amplitude interwell limit cycle oscillations (LCOs) are regarded as an ideal high-output state of multistable vibration energy harvesters. However, chaotic responses, which result in lower output voltages than interwell LCOs, can be observed in bistable vortex-induced vibration energy harvesters (VIVEHs). In this paper, the chaos in bistable VIVEHs is investigated through numerical simulation, theoretical analyses, and experimental validation. The distribution of the periodic solutions obtained by the incremental harmonic balance (IHB) method and chaos judgment using Lyapunov exponents are elucidated. It is found that the bistable VIVEH shows intrawell periodic solutions at high reduced wind speeds (RWSs) and period-doubling bifurcation appears with the periodic solutions turning into chaos with decreasing RWS. Analyses of the influence of nonlinear parameters on the chaotic responses identify the nonlinear stiffness as the dominant factor contributing to the chaos. Meanwhile, the chaotic responses and interwell LCOs would exist at the same RWS with different initial states. Finally, wind tunnel experiments confirm the occurrence of homologous chaotic responses of the bistable VIVEH which feature aperiodic jumping back and forth motion between two potential wells, in agreement with numerical simulations. Overall, this paper provides a framework for analyzing the chaotic responses of bistable VIVEHs, offering valuable insights for complex response mechanism understanding.

Homoclinic Bifurcations and Chaotic Dynamics in a Bistable Vibro-Impact SD Oscillator Subject to Gaussian White Noise

This paper studies the effect of Gaussian white noise on homoclinic bifurcations and chaotic dynamics of a bistable, vibro-impact Smooth-and-Discontinuous (SD) oscillator. First, the SD oscillator is reproduced and generalized by installing a slider on a fixed rod, so the slider is connected by a pair of linear springs initially pre-compressed in the vertical direction to achieve bistable vibration characteristics, and two screw nuts are installed on the rod as two adjustable bilateral rigid constraints to generate the vibro-impact. A discontinuous dynamical equation with a map defined on switching boundaries to represent velocity loss during each collision is derived to describe the vibration pattern of the bistable, vibro-impact SD oscillator through studying the persistence of the unique, unperturbed, nonsmooth, homoclinic structure. Second, the general framework of random Melnikov process for a class of bistable, vibro-impact systems contaminated with Gaussian white noise is derived and employed through the corresponding Melnikov function to obtain the necessary parameter thresholds for homoclinic tangency and possible chaos of the bistable, vibro-impact SD oscillator. Third, the effectiveness of a semi-analytical prediction by the Melnikov function is verified using the largest Lyapunov exponent, bifurcation series, and 0–1 test. Finally, the sensitivity to the initial values of chaos is verified by the fractal attractor basins, and the influence of the Gaussian white noise on periodic and chaotic structures is studied through Poincaré mapping to show the rich dynamical geometric structures.

The Design and Ground Test Verification of an Energy-Efficient Wireless System for the Fatigue Monitoring of Wind Turbine Blades Based on Bistable Piezoelectric Energy Harvesting.

A wireless monitoring system based on piezoelectric energy harvesting (PEH) is presented to provide fatigue data of wind turbine blades in operation. The system comprises three subsystems, each respectively providing the following functions: (i) the conversion of mechanical to electric energy by exploiting the bistable vibration of a composite beam with piezoelectric patches in post-buckling, (ii) harvesting the converted energy by means of a modified, commercial, off-the-shelf (COTS) circuit to feed a LiPo battery and (iii) the battery-powered acquisition and wireless transmission of sensory signals to the cloud to be elaborated upon by the end-user. The system was verified with ground tests under representative operation conditions, which demonstrated the fulfillment of the design requirements. The measurements indicated that the system provided 23% of the required power for fully autonomous operation when subjected to white noise base excitation of 1 g acceleration in the range of 1-20 Hz.

Dynamic Characteristics of Bistable Vibration Energy Harvester Incorporating Electromagnetic Generator

Although various vibration energy harvesters have been designed over the past few decades, efforts to develop efficient, broadband energy harvesters continue. This work provides a detailed insight into a bistable vibration harvester subjected to correlated Gaussian white noise, with the friction between the rack and pinion described by the slip-stick model. Using the harmonic balance method, the frequency response curve of the amplitude under different mass ratios is discussed. The system response will be enhanced with an increased mass ratio for sinusoidal excitation, but not in the case of random excitation. By employing the stochastic average of the energy envelope, the dynamical governing equation of the harvester is solved, and the probability density functions (PDFs) under different damping coefficients, nonlinear stiffness of the restoring force, and excitation intensities are derived. The results are compared with those from Monte Carlo simulations (MCS) and show good accuracy. The results reveal the presence of P-bifurcations. When the nonlinear stiffness and damping coefficient vary, the number of peaks in the PDFs of system displacement and velocity changes. By adjusting the system parameters, the motion of the system can be significantly enhanced.

Characterization of magnetostrictive bi-stable rotational vibration energy harvester with integrated centrifugal effect

Rotational machinery is a common presence in dust still production, and the occurrence of operational failures in components like engines and turbine blades necessitates effective measures. To solve this challenge, remote structural health monitoring using energy harvesting and wireless sensors has been widely employed to realize self-powered sensing. This study proposes a magnet-induced bi-stable rotational energy harvester (REH), which utilizes the centrifugal effect to broaden the effective frequency bandwidth, enabling efficient energy harvesting in complex environments. A comprehensive mathematical model has been established to facilitate the dynamic characteristics of the bi-stable system, taking into account the centrifugal effect. The theoretical results demonstrate that the gap distance of magnetic configuration has great effects on the bi-stable system. Additionally, the centrifugal effect decided by the centrifugal radius and rotational speeds also affects the stable high-energy orbit oscillations. Furthermore, experimental results indicate that the proposed REH can effectively operate within the frequency range of 230–290 rpm, with a maximum RMS voltage of 780 mV and corresponding power of 4.35 mW. These findings validate the performance of the bi-stable magnetostrictive REH with the centrifugal effect and indicate its potential to effectively address the power supply challenges for wireless sensors. Overall, this study presents a promising solution for enhancing the energy harvesting performance of REH and also provides insights into the design of high-efficiency REH by magnet-induced nonlinearity and the centrifugal effect.

Dynamical analysis and design theory for active bistable vibration isolators considering delay effect

Bistable vibration isolators (BVIs), which can undergo intra- and inter-well motions, have recently gained much attention as different motions can lead to different low-frequency isolation properties. To fully exploit the strength of BVIs, feedback actuation is injected into a classic three-spring-two-link bistable structure, and the classic PD control is applied to tune system's stiffness and damping. Moreover, the effect of the inevitable loop delay on BVI performance is considered. Operable regions of control parameters to maintain bistable characteristics and robustness regions where active BVIs are operable regardless of delay perturbations are determined. Besides, bistable dynamics, complicated by the transcendentality caused by delay, are investigated. By taking the BVI as phase zero, the number of variables to be solved is reduced, and an efficient frequency-sweeping-based calculation procedure is proposed. The BVI is evaluated by force and displacement transmissibility, showing that both intra- and inter-well motions benefit vibration isolation. For the former, the BVI yields broadband vibration isolation similar to conventional high-static-low-dynamics-stiffness vibration isolators. For the latter, an isolation valley can occur, resulting in exclusive ultra-low-frequency vibration isolation. Furthermore, properly tuning feedback actuation enhances the vibration isolation performance in both cases, and the often-overlooked loop delay can play a very positive role. Finally, the mechanism of isolation valley is qualitatively elucidated. The presented theories, including control stability analysis, delay-coupled nonlinear dynamical analysis, and beneficial parameter tuning, establish a basic design framework for active BVIs.

A comparative analysis of parallel SSHI and SEH for bistable vibration energy harvesters

The present work focuses on ambient vibration energy harvesting. Specifically, this article deals with bistable piezoelectric energy harvesters (PEHs) which exhibits a wider bandwidth than linear oscillators. These complex systems require an energy extraction circuit (EEC) to rectify their voltage to supply power to autonomous sensors. This EEC needs to be optimized in order to increase the harvested power and even the bandwidth of PEHs. Because of the complex dynamics of bistable PEHs, there is a lack of simple and physically-insightful models in the literature that would allow the understanding and optimization of the extraction circuit. To address this issue, the present work derives closed-form models of a bistable PEH coupled to a passive and an active synchronous EEC: respectively the standard energy harvesting (SEH) circuit and the parallel synchronized switch harvesting on inductor (P-SSHI) circuit. Experimental measurements conducted on a custom bistable PEH demonstrate the validity of the proposed models with a relative error lower than 15% on the harvested power and the bandwidth. The proposed models allow to easily understand the influence of the P-SSHI circuit on the dynamics of a bistable PEH. Moreover, a comparison of the performance of the SEH and the P-SSHI circuits, valid for any bistable generator, is proposed. The latter shows that under low electromechanical coupling and low acceleration amplitude the P-SSHI circuit leads to multiply the maximum harvested power up to 4.3 compared to the SEH circuit, and the bandwidth by a factor of 2.3.

Practical asymmetry and its effects on power and bandwidth performance in bi-stable vibration energy harvesters

Scavenging energy from ambient vibrations using piezoelectric bi-stable energy harvesters (BEHs) has been a research focus in recent years. The typical assumption that BEHs have perfectly symmetric potential profiles is hardly attainable in practice. Unlike previous works which model asymmetry as a quadratic restoring force term, we present a physically quantifiable concept of practical asymmetry degree γ which can be utilized in both theory and experiment. Also, we optimize the nondimensional method by normalizing to the inherent parameters, which guarantees consistent and comparative model analysis. Based on above, a comprehensive study of practical asymmetry’s effect on BEH’s performance is experimentally validated. Results show that for stable inter-well oscillation, asymmetry increases BEH’s output power due to enlarged phase orbit space, but decreases BEH’s bandwidth due to elevated potential barrier. Compared with symmetric BEH, asymmetric BEH improves power by 57.56 % and 26.93 % but reduces bandwidth by 73.81 % and 57.38 % in simulation (γ = 4.08) and in experiment (γ = 4.11), respectively. Initial position in the shallow well improves both power and bandwidth of the asymmetric BEHs. Compared with deep well initial position, shallow well initial position exhibits 41.72 % power improvement and 50.00 % bandwidth increase in experiment (γ = 4.11). Sufficiently large excitation level is required to reach above conclusions, as asymmetric BEHs under small excitations might not reach optimal performance. These results provide instructive insights for designing practical BEHs with improved power and bandwidth performance.

Correction to: Probabilistic maps on bistable vibration energy harvesters

Correction to: Probabilistic maps on bistable vibration energy harvesters

Correction to: Probabilistic maps on bistable vibration energy harvesters

Correction to: Probabilistic maps on bistable vibration energy harvesters

Tailored nonlinear stiffness and geometric damping: Applied to a bistable vibration absorber

A novel device is proposed to obtain arbitrary restoring force characteristics and nonlinear geometric damping. It consists of linear springs and dampers that are compressed along a track. The obtained nonlinear damping and stiffness law depend on the track’s shape. The device is then applied to obtain a nonlinear energy sink (NES) to damp the vibrations of a host system. Both the case of transient vibrations, induced by shock loads, and sustained vibrations, induced by harmonic loads, are studied. For arbitrary stiffness and damping, slow flow dynamics and slow invariant manifolds (SIMs) are derived by applying harmonic balancing and multiple timescales techniques. Under transient vibrations, two performance measures are derived from the SIM, the relative residual energy and the pumping time, and are found for generic nonlinear spring force and nonlinear geometric damping. For sustained vibrations, a load-dependent frequency response (FR) is derived from the SIMs. This FR predicts the occurrence of the efficient strongly modulated responses but also the occurrence of the unfavorable detached responses called isolas, where the NES fails to mitigate and even amplifies vibrations.This research investigates the performance of a conventional cubic NES and a bistable NES (BNES) with nonlinear damping obtained from the proposed device. Especially the BNES with nonlinear damping shows attractive properties, with a high degree of robustness over a wide energy range and a low vibration threshold under transient loading. Under harmonic loads, the nonlinear damping helps reduce the effect of isolas. A novel tuning methodology is proposed to avoid isolas for a range of load magnitudes. The new device opens up a whole range of possibilities regarding energy dissipation through nonlinear damping.

Fast fixed-time sliding mode control of a bistable dual-stage vibration isolator with disturbances

Fast fixed-time sliding mode control of a bistable dual-stage vibration isolator with disturbances

Competitive advantages of a bistable vibration isolator: Cut-off frequency and operational safety near harmful resonance

This study reveals the competitive advantages of a bistable vibration isolator over conventional linear and monostable ones. Generally, reducing stiffness improves vibration isolation performance with a lower cut-off frequency but for the linear vibration isolators involves a large-amplitude oscillation. Nonlinear monostable and bistable vibration isolators have been developed to resolve the contradictory issue of the linear case, reducing both the cut-off frequency and the range of oscillation. However, it has not yet been determined what advantages make a bistable vibration isolator more promising than a monostable one. In this study, equivalent linear, monostable, and bistable vibration isolators were found, and their numerical and theoretical dynamic responses compared directly. First, the cut-off frequency tended to be lower in the order of the bistable, equivalent linear, and monostable vibration isolators. In other words, the bistable system provides a wider vibration isolation bandwidth than the equivalent linear one, whereas the monostable one makes it narrower. Second, the bistable vibration isolator enhanced operational safety in the amplification region thanks to its small force transmissibility, while the monostable one exacerbated the risk. Bifurcation analyses of the nonlinear steady-state oscillations of the bistable and monostable vibration isolators were also performed to identify and investigate the dangerous and safe amplification regions. The results of the analyses clearly demonstrated the superior operational safety of the bistable vibration isolator, particularly in terms of a larger safety margin in the amplification region.

Resonance provocation of improved energy orbit in bi-stable vibration energy harvesters for power enhancement

Bi-stable vibration energy harvesters are advantageous for a wide bandwidth in low frequency ranges, but are confronted with the issue of limited output power. Bi-stability traditionally contains two low- and high-energy orbits; however, this paper reports resonance provocation of the improved energy orbit, which is much higher than the traditional two energy orbits and can be utilized for power enhancement. Theoretically, the enhanced energy orbit is provoked due to an increase in the system’s kinetic energy, achieved by modifying the bi-stable potential energy function from quartic function to quadratic function to utilize the linear resonant restoring force. Experimental results demonstrate that the provocation of the improved energy orbit is frequency selective, and the root mean square voltage is increased by 63.6% in the upward sweep and 188.5% in the downward sweep. For optimal load, the improved energy orbit increases the maximal root mean square voltage by 2.10 times and the maximal average output power by 4.37 times. Meanwhile, the device’s bi-stable bandwidth remains almost unchanged. These results prove that the resonance provocation of the improved energy orbit can refine the power while not sacrificing bandwidth, which is a promising solution to the overall performance improvement for vibration energy harvesters.

Gravity-induced bistable 2DOF piezoelectric vibration energy harvester for broadband low-frequency operation

Gravity-induced bistable 2DOF piezoelectric vibration energy harvester for broadband low-frequency operation

Bi-stable electromagnetic generator with asymmetrical potential wells for low frequency vibration energy harvesting

Efficient energy harvesting from low and broadband frequency has always been a challenging problem. This paper proposes a solution in the form of an electromagnetic bi-stable vibration energy harvester (BVEH) with asymmetric potential barriers, in which the vibrator is attracted to the top magnet and repelled from the bottom magnet. By combining a magnetic spring and a mechanical spring, the BVEH achieves bi-stability with asymmetric potential barriers, enabling large amplitude vibration as the vibrator travels between the two potential wells. The traditional magnetic force model is modified to establish an electromechanical coupling model that accurately predicts the output of the BVEH. Numerical simulation results solved by the Runge-Kutta method show good agreement with experimental results. In addition, a prototype is fabricated and the system parameters are adjusted to achieve high-energy oscillation at the lowest frequency of 4 Hz. Under a sinusoidal excitation with an amplitude of 4 mm, the BVEH's bandwidth is expanded to 6 Hz, and the maximum power can reach 72.76 mW. Finally, the feasibility of the BVEH is demonstrated by powering different electrical appliances. The study provides a new technical approach for energy harvesting under low and broadband frequency vibration excitation.

Development of Bi-Stable Vibration Energy Harvesting System Using Duffing-Type Motion Model

Vibration power generation is an important issue in development of renewable energy. If a vibration system with a maximum possible amplitude is designed, it can be advantageous in improving the vibration power generation efficiency. In this study, we propose a Duffing-type bi-stable vibration energy harvesting system that utilizes the stochastic resonance phenomenon, which can significantly expand the vibration amplitude. We designed the motion rail shape of the bistable vibration model using the Duffing function, and created a Duffing-type wave-shaped motion rail using an acrylic plate. An electromagnetic motor was installed in place of the four rotating wheels below the mass block that moves on the wave-shaped motion rail. When the mass block moves on the rail, it can output a voltage directly from the electromagnetic motor. To verify the performance of the proposed bi-stable vibration energy-harvesting system, a vibration experiment was conducted by combining a random excitation signal that simulates an actual natural environment and intentional periodic excitation signal. Using the experimental results, the stochastic resonance phenomenon and vibration power generation performance of the bi-stable vibration energy-harvesting system were investigated. The stochastic resonance phenomenon can be reliably generated using the bi-stable vibration system proposed in this study, and a large amplitude expansion effect can be obtained in the response vibration of the mass block. In addition, using random signals simulating the natural environment and periodic signals as stimulus signals, vibration experiments were conducted separately for two measurement cases: single excitation and joint excitation. The measurement results showed that under the same input excitation energy, the simultaneous excitation of the two signals generated 82.99% more power than that generated by separate excitation of the two signals. The generation of the stochastic resonance phenomenon by exciting two signals simultaneously has a significant effect on the improvement of the power generation efficiency of the bi-stable vibration energy harvesting system.

Comparative Study of Bistable Vibration Energy Harvester Using Different Elastic Boundary

This paper demonstrates a novel bistable energy harvester coupled with a nonlinear elastic boundary (NEB-BVEH). The nonlinear elastic boundary changes the dynamic response of the bistable vibration energy harvester and improves its performance by providing additional support for the inclined spring through coupled dynamics. This work considers the performance of bistable vibration energy harvesters using different elastic boundary under different excitation amplitudes, including bistable energy harvester with linear elastic boundary (LEB-BVEH) and NEB-BVEH with different horizontal spring stiffness. The comparative results show that the performance of NEB-BVEH and LEB-BVEH is approximately the same under small excitation amplitude. However, NEB-BVEH with adding horizontal springs can significantly improve performance compared to LEB-BVEH under larger excitation amplitude. Results of the investigated case show that the bandwidth of NEB-BVEH is increased by 89.31%. The output power is increased by more than 25%. A comparative study demonstrates the superiority of NEB-BVEH, which is very beneficial for energy harvesting.

Bi-Stable Vibration Power Generation System Using Electromagnetic Motor and Efficiency Improvement by Stochastic Resonance

Bi-Stable Vibration Power Generation System Using Electromagnetic Motor and Efficiency Improvement by Stochastic Resonance<sup />

Study on Dynamic Characteristics of the Bistable Nonlinear Damper

A conventional dynamic vibration absorber based on resonance effect can hardly satisfy the requirement for low-frequency and broadband vibration control in actual engineering. Combined with passive and nonlinear vibration absorption strategy, this study employed nonlinear characteristics of the magnetic force, bistable structure to establish the dynamic model of the main system with a bistable vibration absorber. The nonlinear motion states of the structure under different excitation conditions were analyzed to explore the inherent relation between the chaotic and large amplitude motion and the vibration absorber’s operating performance. The effect laws of the structural parameters on the dynamic characteristics of the nonlinear vibration absorber and the main system were developed to obtain the optimal parameter settings in the case of resonance and off-resonance of the main system. These results provide an insightful theoretical foundation for the optimal design of the nonlinear vibration absorber.