Electrical Load Resistance Research Articles

Nonlinear analysis and power improvement of broadband low-frequency piezomagnetoelastic energy harvesters

A significant impediment to the deploy- ment of vibration-based energy harvesting devices has been the limitation of most low-frequency transduc- ers, usually in the form of unimorph or bimorph can- tileverbeam,toextractenergyfromaverynarrowband- width around the transducer's fundamental frequency. In such devices, a slight deviation from the fundamen- tal frequency causes a significant reduction in the level of harvested power by several orders of magnitudes. Additionally,mostofthecurrentresearcheffortsonthe design of piezoelectric energy harvesters have had lim- ited success in achieving low resonance frequency. To overcome these challenges, we introduce an enhanced broadband low-frequency piezomagnetoelastic energy harvester. This harvester consists of a partially cov- ered piezoelectric cantilever beam with a fixed magnet mass at the top of the magnet tip mass. A nonlinear distributed-parameter model based on Euler-Bernoulli beam theory and Galerkin discretization is developed. This electromechanical model is validated with previ- ous experimental measurements for a specific value of the spacing distance between the two magnets. A para- metric study is performed to determine the effects of the spacing distance between the two magnets on the static position of the harvester, natural frequency, and level of the harvested power. It is demonstrated that a decrease between the two attractive magnets results in a decrease in the natural frequency of the harvester withastrongsofteningbehaviorwhichgivestheoppor- tunity to harvest energy at broadband low-frequency range. The results also show that the presence and importance of the softening behavior depends on the electrical load resistance. In conclusion, the results show that depending on the available low excitation frequency, an enhanced piezoelectric energy harvester can be tuned and optimized by changing the spacing distance between the two tip magnets.

Manufacture and Characterisation of Piezoelectric Broadband Energy Harvesters Based on Asymmetric Bistable Cantilever Laminates

In this paper a bistable asymmetric laminate is manufactured and coupled to a ferroelectric material for potential energy harvesting applications. A cantilever configuration is explored and the harvester response as a function of vibration frequency, vibration level and electrical load resistance examined. The harvester is characterised at low and high vibration levels where the device exhibits either single well oscillations (at low vibration amplitude) or snap-through events (at high vibration amplitude). As the vibration levels increase and the device approaches snap-through it exhibits ‘softening’ where the peak power moves to lower frequencies with differences in power levels during up-sweep and down-sweep of frequencies. Examination of the frequency dependence of power for a range of load resistances indicates a broadening of the harvester performance at higher vibration levels and during snap-through.

Operating characteristics and performance improvements of a 500 W traveling-wave thermoacoustic electric generator

Traveling-wave thermoacoustic electric generator has drawn increasing attention due to its great prospect in energy conversion. In this work, a traveling-wave thermoacoustic electric generator capable of generating about 500W electric power is studied numerically and experimentally. The performances and the operating characteristics of the system under different working conditions are tested and analyzed. The maximum electric powers can be obtained with electric load resistance around 100–120Ω, and the highest thermal-to-electric efficiencies can be achieved at much larger load resistances. The efficiency at low load resistance is relatively small due to the large pressure amplitudes inside the thermoacoustic system, which increases the dissipations. The variation trends of the electric power and the thermal-to-electric efficiency with the load resistance intrinsically result from the changes of the corresponding acoustic impedance of the linear alternators, which determines the output performance of the thermoacoustic engine meanwhile. The distributions of the acoustic power losses are then calculated and firstly illustrated quantitatively. It is shown that the resonator causes most of the acoustic power losses, and the losses in hot heat exchanger, thermal buffer tube, and feedback tube are also significant. The output performance of the system can be improved by increasing the heating temperature and the mean pressure. A maximum electric power of 473.6W and a highest thermal-to-electric efficiency of 14.5% are achieved experimentally when the mean pressure is 2.48MPa and the heating temperature is 650°C. A pair of linear alternators with a larger swept volume and appropriate acoustic impedances is finally designed to couple with the thermoacoustic torus directly. Numerical results show that the maximum electric power can be increased to 718W and 1005W when the mean pressures are kept at 2.48MPa and 3.20MPa, corresponding to the improvements of 42.6% and 29.4% compared with those of the original system.

A Comprehensive 3D Finite Element Model of a Thermoelectric Module Used in a Power Generator: A Transient Performance Perspective

Thermoelectric power generator has potential for small-scale and distributed power generation because of its high durability and scalability. It is very important to realize that the transient behavior of thermoelectric modules (TEM) affects a thermoelectric generator’s response to dynamic working environments. Traditionally, researchers have used simplified models to describe the behavior of thermoelectric modules. In this paper we propose a comprehensive mathematical model that considers the effect of variations of chemical potential and carrier density, which are ignored by traditional models. Finite element models based on this new model are used to simulate the transient behavior of a thermoelectric module subjected to rapid changes in boundary temperature or working load. Simulation results show that transition times of thermoelectric modules affected by temperature change are much longer than those of modules affected by changes in electrical load resistance. Sudden changes in working temperature cause voltage overshoot of the TEM output, which, however, is not observed in responses to sudden changes of load resistance. Comparisons also show there are significant differences between the behavior of TEM predicted by use of this new comprehensive model and that predicted by use of traditional models, particularly for the high-temperature intrinsic ionization region and the low-temperature weak ionization region. This implies that chemical potential and carrier density variations, which are taken into account by this new model but ignored by traditional models, have major effects on the performance of TEM.

Modeling and performance of electromagnetic energy harvesting from galloping oscillations

The modeling and performance of a galloping-based electromagnetic energy harvester are investigated. To convert galloping oscillations into electrical energy, an electromagnetic transducer is used. A set of representative coupled equations that account for the transverse displacement of the bluff body and the induced electromagnetic current are constructed. The galloping force is modeled by using the quasi-steady approximation. The effects of the electrical load resistance on the coupled damping and onset speed of galloping are determined through a linear analysis. It is shown that the electrical load resistance strongly affects the coupled damping and hence the onset speed of galloping of the harvester. For high values of the electrical load resistance, it is demonstrated that the load resistance has a negligible impact on the onset speed of galloping. A nonlinear analysis is then performed to investigate the effects of the electrical load resistance and wind speed on the harvester’s outputs. The nonlinear normal form is first derived and validated with numerical predictions in order to characterize the type of instability for various cross-section geometries. The results show that a very good agreement is obtained between the normal form solutions and numerical predictions near Hopf bifurcation. It is also shown that, for well-defined values of wind speeds, both the transverse displacement amplitude and the generated voltage are increasing with the electrical load resistance. On the other hand, there is an optimum value of the electrical load resistance, which varies with the wind speed, at which the levels of the harvested power are maximized.

Composite piezoelectric spinal fusion implant: Effects of stacked generators.

Spinal fusion surgeries have a high failure rate for difficult-to-fuse patients. A piezoelectric spinal fusion implant was developed to overcome the issues with other adjunct therapies. Stacked generators were used to improve power generation at low electrical load resistances. The effects of the number of layers on average maximum power and the optimal electrical load resistance were characterized. The effects of mechanical preload, load frequency, and amplitude on maximum power and optimal electrical load resistance were also characterized. Increasing the number of layers from one to nine was found to lower the optimal electrical load resistance from 1.00 GΩ to 16.78 MΩ while maintaining maximum power generation. Mechanical preload did not have a significant effect on power output or optimal electrical load resistance. Increases in mechanical loading frequency increased average maximum power, while decreasing the optimal electrical load resistance. Increases in mechanical loading amplitude increased average maximum power output without affecting the optimal electrical load resistance.

A sensor-type PC strand with an embedded FBG sensor for monitoring prestress forces.

Prestressed Concrete Wire and Strand (PC) strands are the most used materials to introduce prestress in a Pre-Stressed Concrete (PSC) structure. However, it is difficult to evaluate the final prestress force of the PC strand after prestressing or its residual prestress force after completion of the structure on site. This impossibility to assess eventual loss of prestress of the PC strand has resulted in a number of serious accidents and even in the collapse of several structures. This situation stresses the necessity to maintain the prestress force residual or after prestressing for the evaluation of the health of the concrete structure throughout its lifespan. Recently, several researchers have studied methods enabling one to verify the prestress force by inserting an optical fiber sensor inside the strand but failed to provide simple techniques for the fabrication of these devices to fulfill measurement performance from the design prestress to failure. Moreover, these methods require the additional installation of electrical resistance strain gages, displacement sensors and load cells on the outer surface of the structure for long-term precise measurement. This paper proposes a method enabling one to evaluate precisely and effectively the prestress force of the PC strand and intends to verify the applicability of the proposed method on actual concrete structures. To that end, an innovative PC strand is developed by embedding a Fiber Bragg Grating (FBG) sensor in the core wire of the PC strand so as to enable short term as well as long term monitoring. The measurement performance of the developed strand is then evaluated experimentally and the reliability of the monitoring data is assessed.

Equivalent circuit method for resonant magnetoelectric effect in disk-shaped laminated composites

A theoretical model based on equivalent circuit analytical method has been presented for the magnetoelectric (ME) effect in disk-shaped laminated composites. The derived expressions for the ME voltage coefficient can be used to describe the frequency response of ME effect under both open circuit and finite electrical resistance load conditions. It was shown that the resonance frequency and resonant ME voltage coefficient increase with the increase in electrical resistance load in disk-shaped ME laminated composite, which is consistent with the observations for plate-shaped one. The theoretical results show good agreement with the experimental results in Tb 0.3 Dy 0.7 Fe 1.92 (Terfenol-D)/Pb(Zr,Ti)O 3 (PZT)/Terfenol-D disk-shaped sandwich laminated composite. This work is significant for designing ME devices and their signal-processing and electronic circuits.

Optimal electromagnetic energy extraction from transverse galloping

A fully coupled electro-fluid-elastic model for electromagnetic energy harvesting from Transverse Galloping is presented here. The model considers a one degree-of-freedom galloping oscillator where fluid forces are described resorting to quasi-steady conditions; the electromagnetic generator is modelled by an equivalent electrical circuit where power is dissipated at an electrical load resistance; the galloping oscillator and the electromagnetic model are coupled appropriately. Two different levels of simplification have been made depending on the comparison between the characteristic electrical and mechanical timescales. The effect of the electrical resistance load on the energy harvested is studied theoretically. For fixed geometry and mechanical parameters, it has been found that there exists an optimal electrical resistance load for each reduced velocity. On the practical side, this result can be helpful to design tracking-point strategies to maximize energy harvesting for variable flow velocity conditions.

Experimental investigation of galloping piezoelectric energy harvesters with square bluff bodies

In this paper, both a baseline galloping piezoelectric energy harvester (GPEH) with a square bluff body and an improved GPEH with an impact bump stop are tested in a wind tunnel in order to determine the system damping, electrical response and limit cycle oscillation (LCO) amplitude. In the baseline GPEH, harvested voltage, LCO amplitude and damping ratio vary with wind velocity and electrical load. They all increase with increasing wind velocity under the same electrical load. Under each wind velocity, the damping ratio increases from the short circuit load, reaches a peak value at the electrical load resulting in a maximum voltage, and reduces the value at the open circuit load. The LCO amplitude shows the opposite trend compared to the damping case. It decreases as the electrical resistance load increases and reaches the minimum value when the damping ratio is highest. A resistance load of 100 kΩ yields a maximum peak power output. The impact stop is introduced to reduce bending stresses and improve the fatigue life of the baseline GPEH. The performance of the improved GPEH depends on the stop design parameters such as gap size, stop location and contact area. Comprehensive tests were conducted to investigate the effect of each parameter on the performance of the improved GPEH and an optimal bump stop configuration was determined. Compared to the expected proportional reduction in both electrical and structural responses, a maximum 70% reduction in LCO amplitude and only a maximum 20% reduction in harvested voltage are achieved in our optimal improved GPEH. The time variable and motion dependent aerodynamic forces acting on the bluff body could contribute to this. In summary, comprehensive experimental evaluations were conducted to characterize the performance of both baseline GPEHs and improved GPEHs. The baseline GPEH service life can be significantly improved by incorporating an impact bump stop. The improved GPEH design provides a practical solution to harvest electricity from wind-induced vibration.

Theoretical modeling and nonlinear analysis of piezoelectric energy harvesting from vortex-induced vibrations

A nonlinear distributed-parameter model for harvesting energy from vortex-induced vibrations of a piezoelectric cantilever beam with a circular cylinder attached to its end is developed and validated with experimental results. A reduced-order model is derived by using the Euler–Lagrange principle and implementing the Galerkin discretization. A van der Pol wake oscillator is used to model the vortex-induced lift force. A nonlinear analysis is performed to determine the required number of modes in the Galerkin discretization. It is demonstrated that a one- or two-mode approximation in the Galerkin approach is not sufficient to evaluate the performance of the harvester. Based on a five-mode approximation in the Galerkin approach, an identification for the van der Pol wake oscillator coefficients is performed. To design efficient piezoaeroelastic energy harvesters that can generate energy at low freestream velocities, further analysis is performed to investigate the effects of the cylinder’s tip mass, length of the piezoelectric sheet, and electrical load resistance on the synchronization region and performance of the harvester. The results show that depending on the operating freestream velocity, the cylinder’s tip mass, length of the piezoelectric sheet, and electrical load resistance can be optimized to design enhanced piezoaeroelastic energy harvesters from vortex-induced vibrations.

Comparison of monolithic and composite piezoelectric material–based energy harvesting devices

This study presents a comparison of the energy harvesting capacity of monolithic and composite piezoelectric materials, especially in the same energy harvesting configuration. The energy harvesting device was composed of a cantilever beam with active piezoelectric materials, a full-bridge rectifier circuit and an electrical load (resistance). Two energy harvesting devices were fabricated, both of which had piezoelectric patches mounted on top and bottom of the cantilever vibrating element. The first energy harvesting device utilized PZT-5H patches as a monolithic piezoelectric material, and the second energy harvesting device used macro-fiber composite patches as a composite piezoelectric material. The vibrating element used in this study was a stainless steel cantilevered beam with the same dimension as the patch. Characteristics of the energy harvesting devices, including generated power, current, and voltage, were compared in frequency domain and evaluated with respect to the electrical load under different excitation levels. In addition, the effects of the natural frequencies of the energy harvesting devices to the harvesting performance were evaluated. The power density (i.e. power over volume) and specific power (i.e. power over mass) of the energy harvesting devices were compared. In addition, the current density (i.e. current over volume) and specific current (i.e. current over mass) were also presented. Finally, the charging and discharging performances of the energy harvesting devices were also evaluated using a polymer Li-ion battery as the electrical load.

Nonlinear characterization of concurrent energy harvesting from galloping and base excitations

An energy harvester is proposed to concurrently harness energy from base and galloping excitations. This harvester consists of a triangular cross-sectional tip mass attached to a multilayered piezoelectric cantilever beam and placed in an incompressible flow and subjected to a harmonic base excitation in the cross-flow direction. A coupled nonlinear-distributed-parameter model is developed representing the dynamics of the transverse degree of freedom and the generated voltage. The galloping force and moment are modeled by using a nonlinear quasi-steady approximation. Under combined loadings and when the excitation frequency is away from the global natural frequency of the harvester, the response of the harvester mainly contains these two harmonic frequencies. Thus, the harvester’s response is generally aperiodic and is either periodic with large period (i.e., period-\(n\)), or quasi-periodic, or chaotic. To characterize the harvester’s response under a combination of vibratory base excitations and aerodynamic loading, we use modern methods of nonlinear dynamics, such as phase portraits, power spectra, and Poincare sections. A further analysis is then performed to determine the effects of the wind speed, frequency excitation, base acceleration, and electrical load resistance on the performance of the harvester under separate loadings.

Piezoelectric energy harvesting from concurrent vortex-induced vibrations and base excitations

We investigate the potential of using a piezoelectric energy harvester to concurrently harness energy from base excitations and vortex-induced vibrations. The harvester consists of a multilayered piezoelectric cantilever beam with a circular cylinder tip mass attached to its free end which is placed in a uniform air flow and subjected to direct harmonic excitations. We model the fluctuating lift coefficient by a van der Pol wake oscillator. The Euler–Lagrange principle and the Galerkin procedure are used to derive a nonlinear distributed-parameter model for a harvester under a combination of vibratory base excitations and vortex-induced vibrations. Linear and nonlinear analyses are performed to investigate the effects of the electrical load resistance, wind speed, and base acceleration on the coupled frequency, electromechanical damping, and performance of the harvester. It is demonstrated that, when the wind speed is in the pre- or post-synchronization regions, its associated electromechanical damping is increased and hence a reduction in the harvested power is obtained. When the wind speed is in the lock-in or synchronization region, the results show that there is a significant improvement in the level of the harvested power which can attain 150 % compared to using two separate harvesters. The results also show that an increase of the base acceleration results in a reduction in the vortex-induced vibrations effects, an increase of the difference between the resonant excitation frequency and the pull-out frequency, and a significant effects associated with the quenching phenomenon.

Comparative modeling of low-frequency piezomagnetoelastic energy harvesters

In order to design efficient low-frequency piezomagnetoelastic energy harvesters, an effective analytical model which considers the effects of the electromechanical coupling and the nonlinear magnetic force is required. In this paper, the harvester consists of a partially covered piezoelectric cantilever beam with a fixed magnet mass at the top of the magnet tip mass. A nonlinear distributed-parameter model based on Euler–Bernoulli beam theory and Galerkin discretization is developed. The used mode shapes in the Galerkin discretization take into account the fact that the magnetic force and the piezoelectric sheet do not cover the whole beam. In addition, we develop an approximated distributed-parameter model that is based on the classical mode shapes of a fully covered piezoelectric cantilever beam in the Galerkin discretization. These distributed-parameter models are compared with a lumped-parameter model and experimental measurements. The results show that the derived distributed-parameter model accurately predicts the experimental measurements and particularly the accompanying softening behavior. On the contrary, it is demonstrated that the approximated distributed-parameter and lumped-parameter models give erroneous predictions of the resonance region, the level of the harvested power, and the softening behavior. In order to investigate the effects of the load resistance and the softening behavior on the performance of the harvester, a parametric study based on the analytically validated model is then performed. The results show that the presence and importance of the softening behavior depends on the electrical load resistance. It is also demonstrated that the presence of the softening behavior plays an important role in the short- and open-circuit configurations.

Optimal Energy Harvesting from a Membrane Attached to a Tensegrity Structure

The feasibility of harvesting energy using polyvinylidene fluoride patches mounted on a vibrating prestressed membrane, itself attached to a tensegrity structure, was investigated. Kinematics of the tensegrity structure and the attached membrane is described and conditions for stable equilibrium for the structure are derived. Nonlinear partial differential equations describing the dynamics of the membrane attached to the tensegrity structure and under the action of a time-dependent transverse pressure are derived using the principle of virtual work. These equations are linearized and the modes of the structure are obtained using the finite element method. These modes are used as basis functions in developing a reduced-order model to obtain the response of the complete structure under the applied transverse dynamic pressure. The polyvinylidene fluoride patch on the structure is connected to an electrical load resistance. The electrical current passing through the load resistance is calculated using Gauss’s law. From this, the amount of energy available for harvesting is estimated. Next, a genetic-algorithm-based optimization is performed to find the polyvinylidene fluoride patch locations, the rest length of the tendons, and the rest dimensions of the membrane, which maximize the amount of energy that can be harvested.

Piezoelectric energy harvesting from hybrid vibrations

The concept of harvesting energy from ambient and galloping vibrations of a bluff body with a triangular cross-section geometry is investigated. A piezoelectric transducer is attached to the transverse degree of freedom of the body in order to convert these vibrations to electrical energy. A coupled nonlinear distributed-parameter model is developed that takes into consideration the galloping force and moment nonlinearities and the base excitation effects. The aerodynamic loads are modeled using the quasi-steady approximation. Linear analysis is performed to determine the effects of the electrical load resistance and wind speed on the global damping and frequency of the harvester as well as on the onset of instability. Then, nonlinear analysis is performed to investigate the impact of the base acceleration, wind speed, and electrical load resistance on the performance of the harvester and the associated nonlinear phenomena that take place. The results show that, depending on the interaction between the base and galloping excitations, and the considered values of the wind speed, base acceleration, and electrical load resistance, different nonlinear phenomena arise while others disappear. Short- and open-circuit configurations for different wind speeds and base accelerations are assessed. The results show that the maximum levels of harvested power are accompanied by a minimum transverse displacement when varying the electrical load resistance.

Modeling and analysis of piezoelectric vibration energy harvesting system using permanent magnetics

Modeling and analyzing of the piezoelectric vibration energy harvester using permanent magnets are systematically investigated to facilitate the evaluation and optimization of such a harvester. We set up a distributed-parameter model for describing nonlinear dynamic behaviors of these harvesters，and present harmonic analytical solution by using harmonic balance method. An analysis is performed using the simulation model to determine the effects of the distance between two magnets, amplitude of acceleration, electrical load resistance on the level of the output power. The optimum resistive loads under different vibration frequencies and accelerations are also compared. The results show that the bistable configuration is applicable to a small excitation case, and the closer to the transition region the small excitation position, the more the power can be harvested. Conversely, the monostable hardening configuration is suited for the large excitation case, the corresponding optimal magnet distance is not close to the transition region. Furthermore, the large amplitude oscillation between two potential wells and small amplitude oscillation within one potential well also bring forth coexisting phenomena of high-energy response and low-energy response; the closer to the transition region the oscillation position, the more obivious the coexisting phenomenon is. It is also demonstrated that exciting frequency is a decisive factor of optimum load resistance.

Modeling and Identification of Circular Cylinder-based Piezoaeroelastic Energy Harvesters

In this paper, we develop a validated nonlinear distributed-parameter model for harvesting energy from vortex-induced vibrations. The harvester consists of a piezoelectric cantilever beam with a circular cylinder attached to its end. By using the Euler-Lagrange principle and implementing the Galerkin discretization, a reduced-order model is derived. Based on a five-mode approximation in the Galerkin approach, an identification for the van der Pol wake oscillator coefficients is performed. Further analysis is performed to investigate the effects of the cylinder's tip mass and electrical load resistance on the synchronization region and performance of the harvester. The results show that, depending on the operating freestream velocity, the cylinder's tip mass can be optimized to design enhanced piezoaeroelastic energy harvesters from vortex-induced vibrations.

Modeling, validation, and performance of low-frequency piezoelectric energy harvesters

Analytical and finite element electromechanical models that take into account the fact that the piezoelectric sheet does not cover the whole substrate beam are developed. A linear analysis of the analytical model is performed to determine the optimal load resistance. The analytical and finite element models are validated with experimental measurements. The results show that the analytical model that takes into account the fact that the piezoelectric patch does not cover the whole beam predicts accurately the experimental measurements. The finite element results yield a slight discrepancy in the global frequency and a slight overestimation in the value of the harvested power at resonance. On the contrary, using an approximate analytical model based on mode shapes of the full covered beam leads to erroneous results and overestimation of the global frequency as well as the level of harvested power. In order to design enhanced piezoelectric energy harvesters that can generate energy at low-frequency excitations, further analysis is performed to investigate the effects of varying the length of the piezoelectric material on the natural frequency and the performance of the harvester. The results show that there is a compromise between the length of the piezoelectric material, the electrical load resistance, and the available excitation frequency. By quantifying this compromise, we optimize the performance of beam–mass systems to efficiently harvest energy from a specified low frequency of the ambient vibrations.