Reliability-Based Design Optimization for Nonlinear Energy Harvesters

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.

Linear and nonlinear piezoelectric devices are introduced to continuously recharge the batteries of the pacemakers by converting the vibrations from the heartbeats to electrical energy. The power requirement of a pacemaker is very low. However, after few years, patients require another surgical operation just to replace their pacemaker battery. Linear low frequency and nonlinear mono-stable and bi-stable energy harvesters are designed according to the especial signature of heart vibrations. The proposed energy harvesters are robust to variation of heart rate and can meet the power requirement of pacemakers.

Infrared astronomy review : Augason, Gordon C., and Hyron Spinrad, Ames Research Center, Moffett Field, California, NASA TM X-1074, March, 1965, 21 p., illus.

This paper investigates a dynamic model and behavior of a novel double-beam piezo–magneto–elastic nonlinear wind energy harvester (DBPME-WEH). The DBPME-WEH is a double-beam structure, which contains the magnet-induced bistable nonlinearity to enhance the performance of the galloping-based vibration energy harvesting. The corresponding governing equations of motion are formulated, and the numerical results based on the equations are validated by a series of the wind tunnel experiments. Both the numerical and experimental results show that the DBPME-WEH outperforms the linear double-beam piezoelectric wind energy harvester, significantly reducing the cut-in speed. To understand the nonlinear dynamic behavior of the proposed energy harvester, this study performs the numerical investigations of the time-domain responses, phase portraits and frequency spectrums of the DBPME-WEH under selected wind speeds. The intra-well, chaotic and inter-well oscillations are discovered with respect to low, medium and high wind speeds intervals, respectively. The parametric study is performed to uncover the influences of the beams stiffness ratio, effective mass ratio and the width of the bluff body that help developing the insights of the effective design of the DBPME-WEH.

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.

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.

We study the dynamics of h-BN monolayers by first performing ab-initio calculations of the deformation potential energy and then solving numerically a Langevine-type equation to explore their use in nonlinear vibration energy harvesting devices. An applied compressive strain is used to drive the system into a nonlinear bistable regime, where quasi-harmonic vibrations are combined with low-frequency swings between the minima of a double-well potential. Due to its intrinsic piezoelectric response, the nonlinear mechanical harvester naturally provides an electrical power that is readily available or can be stored by simply contacting the monolayer at its ends. Engineering the induced nonlinearity, a 20 nm device is predicted to harvest an electrical power of up to 0.18 pW for a noisy vibration of 5 pN.

Aeroelastic energy harvesting can be used to power wireless sensors embedded into bridges, ducts, high-altitude buildings, etc. One challenging issue is that the wind speed in some application environments is low, which leads to an inefficiency of aeroelastic energy harvesters. This paper presents a novel nonlinear magnetic-coupled flutter-based aeroelastic energy harvester (FAEH) to enhance energy harvesting at low wind speeds. The presented harvester mainly consists of a piezoelectric beam, a two-dimensional airfoil, two tip magnets and two external magnets. The function of magnets is to reduce the cut-in wind speed of the FAEH and enhance energy harvesting performance at low wind speeds. A theoretical model is deduced based on Hamilton’s principle, theory of aeroelasticity, Kirchhoff’s laws and experimental measurements, etc. A good agreement is found between numerical simulation and experimental results, which verifies the accuracy of the theoretical model. Stability analysis is provided to determine the characteristics of the presented harvester. More importantly, it is numerically and experimentally verified that the presented harvester has a much lower cut-in wind speed (about 1.0 m s−1) and has a better energy harvesting performance at a low wind speed range from 1.0 m s−1 to 2.9 m s−1, when compared with traditional FAEHs.

Energy efficiency maximization in UAV communication networks with nonlinear energy harvesting

In this work, we present STONEHENGE - Suite for nonlinear analysis of energy harvesting systems, a comprehensive toolbox engineered to study nonlinear piezoelectric vibration energy harvesters. These harvesters can harness kinetic energy from the environment and convert it into electricity using the piezoelectric effect. By introducing nonlinearity through strategically placed magnets, their efficiency is enhanced across a wide frequency spectrum. However, it comes at the cost of increasing complexity in system dynamics. To investigate this complexity and comprehend the potential of nonlinear energy harvesting, the STONEHENGE library was created. It is tailored to analyze the harvesting performance and dynamic behavior of these systems and allows users to explore and characterize system dynamics across a diverse range of physical parameters and excitation conditions using advanced numerical simulations. The toolbox encompasses six key modules, (i) initial value problem, analysis of system behavior from initial conditions; (ii) dynamic animation: which provides visual representations of system dynamics, aiding in intuitive understanding and interpretation; (iii) nonlinear tools: equips users with tools to dissect and comprehend the nonlinear aspects of vibration harvesting systems, essential for comprehensive analysis; (iv) sensitivity analysis: facilitates the assessment of how system behavior responds to variations in parameters, offering insights into its robustness and performance under different conditions; (v) stochastic simulation: allows for the exploration of system behavior under stochastic excitation, crucial for understanding real-world operating conditions; (vi) chaos control: offers methods for mitigating chaotic behavior within the system, enhancing predictability and stability. Utilizing a bistable oscillator as a benchmark, STONEHENGE aims to serve as a valuable resource for the development and refinement of both existing and emerging nonlinear vibration-based energy harvesting systems. By providing a comprehensive toolkit for analysis and characterization, STONEHENGE seeks to catalyze advancements in this field, ushering in an era of more efficient and sustainable energy harvesting technologies. Moreover, this library was developed to be easily adaptable to different dynamic systems and can contribute to different application fields.

A vibratory energy harvesting absorber using integration of a lever-enhanced nonlinear energy sink and a levitation magnetoelectric energy harvester

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.

This paper investigates the optimal power minimization design of simultaneous wireless information and power transfer systems under non-linear energy harvesting (EH) model, where a multi-antenna hybrid access point (H-AP) simultaneously transmits information and power to multiple heterogeneous users, such as information-energy receivers (IERs), information receivers (IRs), and ERs. Power splitting (PS) receiver architecture is adopted at all IERs. In order to achieve green system design, an optimization problem is formulated to minimize the transmit power of H-AP subject to the required signal-to-interference-plus-noise ratios (SINRs) constraints at IERs and IRs, and the harvested energy constrains at IERs and ERs, by jointly optimizing the beamforming vector at H-AP and the PS ratios at IERs. Since the problem is nonconvex and the employ of the non-linear EH model makes it more difficult to solve, the semidefinite relaxation and variable substitutions are used to handle it. For some cases, we theoretically prove that the globe optimal solution can be guaranteed by using our method, and for rest cases, we discuss its optimality via simulations. Numerical results show that although the traditional linear EH model is feasible for the practical EH circuits in some cases, the corresponding system consumes more transmit power than that under the non-linear model EH. Moreover, the effects of the numbers of users, the required SINRs, and the harvested energy on the system transmit power are also discussed.

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

In this paper, the problem of joint mode switching and power adaptation is studied for simultaneous wireless information and power transfer (SWIPT) over a fading channel. The receiver dynamically switches between information decoding (ID) and energy harvesting (EH) modes while the transmitter dynamically adapts the transmit power. Considering the nonlinearity of practical EH circuits, a realistic nonlinear EH model is adopted rather than the idealistic linear EH model. To characterize the ultimate performance tradeoff between ID and EH, an optimization problem is formulated to maximize the average harvested energy under the constraints on the average achievable rate and the average transmit power, which is a nonconvex and combinatorial problem. To solve this problem, first, the optimal power adaptation scheme for the nonlinear EH receiver that operates only in the EH mode is proposed. Using this scheme, the jointly optimal solution for the mode switching and power adaptation is then derived. By comparing the obtained results to the existing results, various useful and interesting insights into the optimized SWIPT system with nonlinear EH are presented. An important insight into the impact of nonlinear EH is that, to exploit the high energy conversion efficiency of the nonlinear circuit, the EH mode has to be selected only in the moderate range of channel gains. Also, in the EH mode, the power has to be adapted to the short-term power threshold only for the moderate channel gains.