STONEHENGE – A toolbox for nonlinear vibration energy harvesting

A new concept of speed amplified nonlinear electromagnetic vibration energy harvester through fixed pulley wheel mechanisms and magnetic springs

Nonlinear vibration energy harvester: Design and oscillating stability analyses

A novel nonlinear structure with adjustable stiffness, damping and inertia is proposed and studied for vibration energy harvesting. The system consists of an adjustable-inertia system and X-shaped supporting structures. The novelty of the adjustable-inertia design is to enhance the mode coupling property between two orthogonal motion directions, i.e., the translational and rotational directions, which is very helpful for the improvement of the vibration energy harvesting performance. Weakly nonlinear stiffness and damping characteristics can be introduced by the X-shaped supporting structures. Combining the mode coupling effect above and the nonlinear stiffness and damping characteristics of the X-shaped structures, the vibration energy harvesting performance can be significantly enhanced, in both the low frequency range and broadband spectrum. The proposed 2-DOF nonlinear vibration energy harvesting structure can outperform the corresponding 2-DOF linear system and the existing nonlinear harvesting systems. The results in this study provide a novel and effective method for passive structure design of vibration energy harvesting systems to improve efficiency in the low frequency range.

In order to effectively take advantage of stiffness nonlinearities in vibration energy harvesters, the harvesters must be appropriately designed to ensure optimum direct current (DC) power generation. Yet, such optimization has only previously been investigated for alternating current (AC) power generation although most electronics demand DC power for their functioning. Moreover, real world excitations contain stochastic contributions combined with periodic components that challenges conventional approaches of investigation that only give attention to the harmonic excitation parts. To fill in the knowledge gap, this research undertakes comprehensive simulations to begin formulating conclusive understanding on the relationships between rectified power generation and nonlinear energy harvester system characteristics when the platforms are subjected to realistic combinations of harmonic and stochastic excitations. According to the simulation results, the rectified power demonstrates clear dependence on the load resistance in the unique limiting cases of complete or no stochastic excitation. When the excitation vibrations include both harmonic and stochastic components, the optimal resistance to maximize DC power exhibits a smoothly correlated but nonlinear change between the limiting case values of the resistance. The results of this investigation provide direct evidence of the intricate relationships among peak DC power, optimal resistive loads, and the nonlinear energy harvester design, and encourage continued study for direct analytical expressions that define such relationships.

Bistable vibration energy harvesters have been comprehensively and thoroughly studied for their outstanding energy harvesting capabilities. The lever mechanism offers a straightforward and effective solution for realizing bistable systems. Neglecting dynamical characterization of such harvesters would lead to unanticipated nonlinear behaviors that impair performance. Thus, this paper proposes a nonlinear lever-type vibration energy harvester with a series-connected RLC circuit. First, a bistable energy harvester is designed by introducing negative stiffness. The theoretical model has been established and is validated by numerical and experimental results. Second, the relationship between the equivalent stiffness and the magnet space is studied, based on which dynamic responses under different magnet spaces are then analyzed by the bifurcation diagram. According to the Poincaré map, chaos can be perceived. The cause of the chaos is figured out as a period-doubling bifurcation through the phase trajectory. Third, potential energy with various lever pivot positions is compared, indicating that a higher potential energy well leads to interwell oscillations, and chaos is highly related to the pivot position. Finally, the power generated is discussed by altering the RLC circuit's resonant frequency and resistance value. The average power is capable of achieving 3.22 mW. Overall, this paper establishes the theoretical foundation for investigating the dynamic characteristics of lever-based bistable energy harvesters, as well as the influence of RLC circuit loading on power output performance.

Leveraging smooth nonlinearities in vibration energy harvesters has been shown to improve the potential for kinetic energy capture from the environment as a transduced, alternating flow of electrical current. While researchers have closely examined the direct current power delivery performance of linear energy harvesters, there is a clear need to quantify the direct current power provided by nonlinear harvester platforms, in particular those platforms having bistable nonlinearities that are shown to have advantages over other smooth nonlinearities. In addition, because real world excitations are neither purely harmonic nor purely stochastic, the influences of an arbitrary combination of such excitation mechanisms on power delivery must be uncovered. To bring needed light to these roles and opportunities for nonlinear energy harvesters to provide direct current electrical power for numerous applications, this research formulates a new analytical approach to characterize simultaneous harmonic and stochastic mechanical and electrical responses of nonlinear harvester platforms subjected to realistic base excitation. Based on the outcomes of analytical, numerical, and experimental studies, it is found that additive stochastic excitation may result in direct current power enhancement via perturbation from a low amplitude state particularly at low frequencies or reduce the direct current power by preventing persistent snap-through response often at higher frequencies. When the noise standard deviation is greater than the harmonic amplitude by approximately two times, the advantages to direct current power generation are more often realized.

A nonlinear hybrid piezoelectric (PE) and electromagnetic (EM) energy harvester is proposed, and its working model is established. Then the vibration response, output power, voltage and current of nonlinear hybrid energy harvester subjected to harmonic excitation are derived by the method of harmonic balance, and their normalized forms are obtained by the defined dimensionless parameters. Through numerical simulation and experimental test, the effects of nonlinear factor, load resistance, excitation frequency and the excitation acceleration on amplitude and electrical performances of hybrid energy harvester are studied, which shows that the numerical results are in agreement with that of experimental tests. Furthermore, it can be concluded that the bigger nonlinear factor, the lower resonant frequency; moreover, there is an optimal nonlinear factor that make the harvester output the maximum power. In addition, the output power of nonlinear hybrid energy harvester reaches the maximum at the optimal loads of PE and EM elements, which can be altered by the excitation acceleration. Meanwhile, the resonant frequency corresponding to the maximum power rises firstly and then falls with PE load enhancing, while it rises with EM load decreasing; furthermore, the frequency lowers with the acceleration increasing. Besides, the larger acceleration is, the bigger power output and the wider 3 dB bandwidth are. Compared with performances of linear hybrid energy harvester, the designed nonlinear energy harvester not only can reduce the resonant frequency and enlarger the bandwidth but also improve the output power.

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.

Data-driven modelling and dynamic analysis of the multistable energy harvester with non-Gaussian Lévy noise

This paper presents reliability-based design optimization (RBDO) and experimental validation of the purely mechanical nonlinear vibration energy harvester we recently proposed. A bi-stable characteristic was embodied with a pre-stressed curved cantilever substrate on which piezoelectric patches were laminated. The curved cantilever can be simply manufactured by clamping multiple beams with different lengths or by connecting two ends of the cantilever using a coil spring. When vibrating, the inertia of the tip mass activates the curved cantilever to cause snap-through buckling and makes the nature of vibration switch between two equilibrium positions. The reliability-based design optimization study for maximization of power density and broadband energy harvesting performance is performed. The benefit of the proposed design in terms of excellent reliability, design compactness, and ease of implementation is discussed. The prototype is fabricated based on the optimal design result and energy harvesting performance between the linear and nonlinear energy harvesters is compared. The excellent broadband characteristic of the purely mechanical harvester will be validated.

We study the effect of an amplification mechanism in a nonlinear vibration energy harvesting system where a ferromagnetic beam resonator is attached to the vibration source through an additional linear spring with a damper. The beam moves in the nonlinear double-well potential caused by interaction with two magnets. The piezoelectric patches with electrodes attached to the electrical circuit support mechanical energy transduction into electrical power. The results show that the additional spring can improve energy harvesting. By changing its stiffness, we observed various solutions. At the point of the optimal stiffness of the additional spring, the power output is amplified a few times depending on the excitation amplitude.

The operational bandwidth of Vibration Energy Harvesters (VEH) is area of concern due to stochastic, time-varying, random and multi-frequency nature of available environmental vibrating sources. Most of the VEH have narrow bandwidth providing usable power at specific frequencies. Efforts have been made to increase the frequency range by introducing non-linear structures and techniques. In this paper, multi-band output of the non-linear Piezoelectric Energy Harvester (PEH) is transformed into single wider band output using additional non-linear phenomenon. Dual region operation of PEH results into two separate band output. First region is the outcome of beam resonance and Centre of Gravity (CoG) shift whereas second region is due to the non-linear behaviour of cylinders. In this work, these separate bands are merged to form a single wider band. For merging these two bands and enhancing the bandwidth of PEH, additional phenomenon is introduced using two permanent magnets. A varying magnetic field by changing the distance between magnets changes stiffness of the cantilever beam and that leads to a change in the resonant frequency of band-I. Thus, the overall process shifts band-I towards band-II. In this work, the two separate bands are merged to have one wider band providing 53.22% more frequency coverage than our previous work with a bandwidth of 47.5 Hz. This band includes vibrational frequency range of 25.65–73.15 Hz at 1.4 g acceleration. Cylinder material and its effect with magnetic interaction is also studied. The magnetic force between two permanent magnets is measured experimentally. Effect of magnetic force on centre resonant frequency of beam is compared with experimental and simulated results. Effect of magnetic force on bandwidth of the device is studied.

Modeling and experimental verification of a fractional damping quad-stable energy harvesting system for use in wireless sensor networks

Improved energy harvesting by enhanced nonlinearities: New phenomena and experimental demonstration

Nonlinear multi-stable piezoelectric energy harvesters show broadband frequency spectra and excellent energy harvesting performance, owing to their high output power related to inter-well transitions. However, existing quad-stable piezoelectric energy harvesters contain too many structural parameters, which makes the systems clumsy, and increases the difficulties of dynamic analysis and structural optimization. Herein, a nonlinear quad-stable piezoelectric energy harvester, with only one external magnet, is proposed based on the magnetic force characteristics between a ring magnet and a rectangular magnet. Under selected structural parameters, as the magnet spacing increases, the stability characteristic of the harvester changes from quad-stability to bi-stability, and then to mono-stability. The transformation of the stability characteristic results from the changes in the variation rate of the vertical magnetic force. Subsequently, under the filtered Gaussian white noise within the frequency range of 0–120 Hz, the energy harvesting performance of the harvester is simulated by the classic fourth-order Runge-Kutta method. Simulation results show that the performance of the harvester under the quad-stable structural parameters is better than that under the bi-stable structural parameters, independent of whether the excitation acceleration is small or large. This result is related to the potential well characteristics under the quad-stable and bi-stable structural parameters. More specifically, the potential well depths under the quad-stable and bi-stable structural parameters are almost the same, but the distance between the two outer potential wells under the quad-stable structural parameters is larger than that under the bi-stable structural parameters. Finally, a fabricated prototype is used to measure the experimental performance of the harvester. The experimental data and the estimated data share the same trend. This study provides a new conception and technical method for the design, optimization, and application of quad-stable piezoelectric energy harvesters.