Linear Harvesting Research Articles

Improving the performance of wind energy galloping harvesting with magnetic coupling

In a realistic environment, the wind speed generally is relatively low, which impedes the further promotion of energy harvesting efficiency. This letter proposes an advanced monostable galloping-based energy harvester (AM-GEH), in which magnetic coupling is introduced to improve harvesting efficiency. By arranging a magnet at the beam tip and three magnets on the arch-shaped fixture, the stiffness of the structure will be softened, which is beneficial for generating large-amplitude deflection for low-speed wind. It is designed so that the middle magnet provides a repulsive force, while the magnets at the two sides provide attractive forces. The combined forces could make the system keep a monostable one, but with a wide flat potential energy. The parameter analysis is carried out to investigate the influence of wind speed and impedance on the output power. For validation, corresponding experiments were carried out. We compare this configuration with the linear galloping-based energy harvester (L-GEH) and the weak-coupled monostable galloping-based energy harvester (WM-GEH). The experimental results show that the cut-in wind speed of AM-GEH is decreased by 55% and 18.2%, respectively, and its RMS voltage is increased by 69.92% and 14.7%, respectively.

Performance Analysis of SWIPT for Intelligent Reflective Surfaces for Wireless Communication

The performance of simultaneous wireless information and power transfer (SWIPT) is investigated for an intelligent reflective surface (IRS)-aided wireless system. Tight bounds for the achievable rate and harvested energy are derived in closed-form for the time-switching (TS) and power-splitting (PS) protocols by adopting linear/non-linear energy harvesting models. The achievable rate-energy trade-off of IRS-aided SWIPT is quantified, and the effects of phase-shift quantization at the IRS are investigated. The impact of TS/PS factors, the number of reflective elements, reflective coefficients, and linear versus non-linear energy harvesting models is also investigated through analytical results and Monte-Carlo simulations.

A Review of Piezoelectric Vibration Energy Harvesting with Magnetic Coupling Based on Different Structural Characteristics.

Piezoelectric vibration energy harvesting technologies have attracted a lot of attention in recent decades, and the harvesters have been applied successfully in various fields, such as buildings, biomechanical and human motions. One important challenge is that the narrow frequency bandwidth of linear energy harvesting is inadequate to adapt the ambient vibrations, which are often random and broadband. Therefore, researchers have concentrated on developing efficient energy harvesters to realize broadband energy harvesting and improve energy-harvesting efficiency. Particularly, among these approaches, different types of energy harvesters adopting magnetic force have been designed with nonlinear characteristics for effective energy harvesting. This paper aims to review the main piezoelectric vibration energy harvesting technologies with magnetic coupling, and determine the potential benefits of magnetic force on energy-harvesting techniques. They are classified into five categories according to their different structural characteristics: monostable, bistable, multistable, magnetic plucking, and hybrid piezoelectric–electromagnetic energy harvesters. The operating principles and representative designs of each type are provided. Finally, a summary of practical applications is also shown. This review contributes to the widespread understanding of the role of magnetic force on piezoelectric vibration energy harvesting. It also provides a meaningful perspective on designing piezoelectric harvesters for improving energy-harvesting efficiency.

Potential of a vibro-impact nonlinear energy sink for energy harvesting

The energy harvesting potential of a vibro-impact nonlinear energy sink (VINES) is investigated. Applying Signorini’s contact law, the non-smooth dynamics is first formulated in a measure differential complementarity problem and treated using a Moreau-Jean scheme adapted with an energy-conserving integration method. The resulting scheme thus shows a good energy preservation property, allowing one to calculate the energy flow of the system in high precision. Exhaustive discussions are then carried out regarding the energy harvesting performance of the proposed VINES harvester, as well as their dependence on the underlying vibro-impact induced response regimes, under both transient and steady-state responses. It is demonstrated that the vibro-impact is responsible for achieving targeted energy transfer in the transient response or controlling the regimes in the steady-state response, to improve significantly the harvesting efficiency. Moreover, a properly designed VINES, working with 1–2 impacts per cycle, is capable for effective broadband energy harvesting over a wide amplitude and frequency range. Two specific considerations are also performed to evaluate further the generality and efficacy of the proposed harvester, and it is proved the VINES can provide higher energy density than the classical linear or cubic NES harvesters, and its effectiveness could be robust over a certain low level of noise.

Nonlinear dynamics and parametric study of snap through electromagnetic vibration energy harvester using multi-term harmonic balance method

Abstract Vibration energy harvester (VEH) has proven to be a favorable potential technique to supply continuous energy from ambient vibrations and its performance is greatly influenced by the design of potential structures. A snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises of three springs that are configured so that the potential energy of the system has two stable equilibrium points. In this work, a harmonically base excited snap-through electromagnetic vibration energy harvester is investigated by analytical and semi-analytical method. The approximate analytical outcomes are qualitatively and quantitatively supported by semi-analytical method using multi-term harmonic balance method (MHBM).The bifurcation diagram of response current shows that snap-through electromagnetic vibration energy harvesters exhibits periodic intrawell, interwell and chaotic motion when the system parameters are varied. The influence of system parameters on the response of snap-through electromagnetic vibration energy harvester are examined. Nonlinearity produced by the snap-through oscillator improves energy harvesting so that the snap-through electromagnetic energy harvester can outperform the linear energy harvester in the similar size under harmonic excitation. A fitness function was formulated and optimization of the selected parameters was done using genetic algorithm. The parametric optimization leads to a considerable improvement in the harvested current from the system.

Benefiting wireless power transfer scheme in power domain based multiple access: ergodic rate performance evaluation

Power domain based multiple access scheme is introduced in this paper, namely Non-orthogonal multiple-access (NOMA). We deploy a wireless network using NOMA together with a wireless power transfer (WPT) scheme for dedicated user over Nakagami-$m$ fading channel. When combined, these promising techniques (NOMA and WPT) improve the system performance in term of ergodic performance at reasonable coefficient of harvested power. However, fixed power allocation factors for each NOMA user can be adjusted at the base station and it further provide performance improvement. We design a new signal frame to deploy a NOMA scheme in WPT which adopts a linear energy harvesting model. The ergodic capacity in such a NOMA network and power allocation factors can be updated frequently in order to achieve a fair distribution among NOMA users. The exact expressions of ergodic capacity for each user is derived. The simulation results show that an agreement between analytic performance and Monte-Carlo simulation can be achieved.

A new concept of frequency-excitation-up conversion to improve the yield of linear piezoelectric generators

A new and novel frequency-excitation up-conversion (FEUC) mechanism achieved by converting low-frequency excitation into friction-induced vibration (FIV) is proposed to improve the output power of linear piezoelectric energy harvesters at ultra-low ambient frequencies. For comparison, a conventional resonant energy harvester and an impact-driven energy harvester are created, the output power is measured at the resonant frequency under a 0.5 g driving acceleration. Then, a friction system driven by reciprocating sliding and capable of generating FIV is established. The driving reciprocating is equivalent to the low-frequency ambient vibration, and a single piezoelectric cantilever beam is added to the friction system for energy recovery. The results show that, compared with the impact-driven energy harvester, the vibration frequency can be increased hundreds of times, and the excitation level can be improved several orders of magnitude by the friction nonlinearities. The impedance of the energy harvester is reduced significantly due to a sharp increase in the vibration frequency. In addition, the open-circuit voltage amplitude is not substantially lowered due to the significantly increased excitation level, even though the piezoelectric cantilever beam operates in a high-frequency condition and in the absence of resonance. Therefore, the output power is dramatically improved. The effectiveness and superiority of the FEUC strategy proposed in this work has been demonstrated.

Dynamics of a Stage-Structured-Prey and Predator Model with Linear Harvesting of Mature Prey and Predator

In this paper we have studied the dynamical behaviors of stage-structured-prey and predator model with linear harvesting of both mature prey and predator. Optimal harvesting policy, positivity, boundedness and Hopf-bifurcation have been studied. Finally, some graphical and numerical simulations are given in order to validate our analytical and theoretical findings.

Leveraging circuit theory and nonlinear dynamics for the efficiency improvement of energy harvesting

We study the performance of vibrational energy harvesting systems with piezoelectric and magnetic inductive transducers, assuming the power of external disturbance concentrated around a specific frequency. Both linear and nonlinear harvester models are considered. We use circuit theory and equivalent circuits to show that a large improvement in both the harvested energy and the power efficiency is obtained, for linear systems, through a proper reactive modification of the load. For nonlinear systems, we use methods of nonlinear dynamics to derive analytical formulae for the output voltage, the harvested energy and the power efficiency. We show that also for the nonlinear case, the modified load significantly boosts the performance.

Efficiency enhancement of electromagnetic energy harvesters for high‐rise buildings

Because the vibration of buildings and bridges is often small in amplitude, low in frequency, and wide in frequency bandwidth, designing a conventional energy harvester with the natural frequency low enough to coincide with the low excitation usually accompany with very large mass and volume. However, it is very important to use portable energy harvester (usually with higher natural frequency) to obtain energy for wireless devices. If portable energy harvesters were used directly on high-rise buildings, the efficiency would be very low. To solve this problem, we propose a simple device to implement portable energy harvester in high-rise building application environment with a high efficiency. It is an intermediate spring-mass system to be installed between the energy harvester and the underlying building. The crux of this device is to enhance the vibration amplitude of the oscillating mass of energy harvesters, so that more energy can be harvested. By changing the degree of freedom (DOF) and stiffness of the intermediate device, the performance of energy harvester can be drastically enhanced. The effects of the parameters of the device for the harvesting performance have been identified using the Lyapunov method, and the conclusion has been verified using four earthquake ground motions. Applications to 100-story buildings are used to demonstrate the efficiency of the proposed intermediate device. In the illustrative examples, this device can increase the generated energy of linear electromagnetic energy harvester (EMEH) up by several hundred times.

Linear electromagnetic energy harvester system embedded on a vehicle suspension: From modeling to performance analysis

Although linear electromagnetic energy harvester (LEH) is a promising technique for converting energy in a vehicle suspension, due to the large displacements, one of the main drawbacks of the solutions inside the vehicle is still their size and complexity. To address this issue, this paper focuses on the design and fabrication of a fully embedded LEH without any modification of the suspension initial structure. After a determination of the electrical, mechanical and electromechanical parameters using a Finite Element analysis, the dynamic efficiency is highlighted with a global Bond Graph model. This formalism is well adapted to simulate energy transfers inside multiphysic systems and to reduce the computational time, whereas the finite element model is not exploitable for a complete suspension simulation. In order to validate the Bond Graph simulation results, an embedded prototype has been built and tested in a laboratory environment. The embedded LEH system delivers around 10 W for a solicitation of linear velocity of 1 m/s which is sufficient to power a classical electronic circuit which is in good correlation with the measured ones and significant power has been obtained.

Periodic Oscillating Dynamics for a Delayed Nicholson-Type Model with Harvesting Terms

In this manuscript, a delayed Nicholson-type model with linear harvesting terms is investigated. Applying coincidence degree theory, we establish a sufficient condition which guarantees the existence of positive periodic solutions for the delayed Nicholson-type model. By constructing suitable Lyapunov functions, a new criterion for the uniqueness and global attractivity of the periodic solution of the Nicholson-type delay system is obtained. The derived results of this article are completely new and complement some previous investigations.

Dynamical behavior of a delayed prey-predator-scavenger system with fear effect and linear harvesting

In this paper, we propose a delayed prey-predator-scavenger system with fear effect and linear harvesting. First, we discuss the existence and stability of all possible equilibria. Next, we investigate the existence of Hopf bifurcation of the delayed system by regarding the gestation period of the scavenger as a bifurcation parameter. Furthermore, we obtain the direction of Hopf bifurcation and the stability of bifurcating periodic solutions by using the normal form theory and the central manifold theorem. In addition, we give the optimal harvesting strategy of the delayed system based on Pontryagin’s maximum principle with delay. Finally, some numerical simulations are carried out to verify our theoretical results.

Three-dimensional formulation of a strain-based geometrically nonlinear piezoelectric beam for energy harvesting

In this paper, the authors introduce a model of a strain-based geometrically nonlinear piezoelectric beam for modeling energy harvesters. A nonlinear shear-underfomable 3-D Rayleigh’s beam theory is used to model the displacement fields and can be considered as an interesting alternative to linear and highly nonlinear models commonly presented in the literature. The nonlinearities are introduced to reproduce the behavior of the flexible structure, since moderate to large displacements can occur in response of external loading conditions. The finite element method is used to model the piezolaminated bimorph configuration. Each finite element consists of two piezoelectric energy harvesters embedded or perfectly bonded to an elastic substrate. The electromechanical coupling includes axial and flexural effects as well as additional term that comes from the nonlinearity incorporated into the strain tensor. Additionally, the authors explore briefly two topics for linear harvesters: the influence of the electric domain on the structural properties and, the performance of the harvester near resonance in term of electric power output of a purely resistive network. As a validation case, a cantilevered piezoelectric energy harvester under base excitation is modeled. Alongside, the response to gust of a harvester embedded in a wing structure is analyzed.

Deterministic and Stochastic Research of Cubic Population Model with Harvesting

A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting are first discussed in the deterministic model. A Fokker–Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker–Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises, respectively.

A wide band nonlinear dual piezoelectric cantilever energy harvester coupled by origami

Since the traditional linear piezoelectric vibration energy harvester has narrow energy conversion frequency band and low energy conversion, a wide band nonlinear dual piezoelectric cantilever energy harvester coupled by origami is proposed. Apart from using two piezoelectric cantilevered beams to broaden the working frequency band of the device, the nonlinear origami component is introduced into the upper and lower beams to realize the dynamic coupling of the two piezoelectric beams. The origami structure can change the stiffness and increase the nonlinearity of the system by dynamic folding, so as to further broaden the frequency band and increase the output power. The structure of the proposed energy harvester is designed. Based on the Euler Bernoulli beam theory, Hamilton principle and the dynamic analysis of origami component, the electromechanical coupling dynamic model of two piezoelectric beam subsystems is established, and the approximate solutions of the output voltage and output power of each subsystem are obtained by harmonic balance method. The numerical simulation of each subsystem is implemented by the Runge–Kutta method, and the influences of excitation frequency and amplitude on the output voltage and power of each subsystem are explored respectively. The results show that this energy harvester that has a nonlinear characteristics of hardening stiffness can significantly broaden the working frequency band of each piezoelectric beam, and the maximum voltage value is about 1.2 V. Via the simulated analysis of motion, it is further proven that the proposed energy harvester has strong nonlinear characteristics. Furthermore, the coupling position of origami component on the voltage output is explored and the optimal coupling position is determined. Finally, the experimental results show that both of two beams can obtain effective voltage output between 0.5 and 0.6 V in the frequency range of 0–50 Hz, which validates the effectiveness and correctness of the simulation model.

Modeling the Ecological Dynamics of a Three-Species Fish Population in the Chesapeake Bay

We present an inquiry-based project that is designed for a mathematical modeling class of undergraduate junior or senior students. It discusses a three-species mathematical model that simulates the biological interactions among three important fish species in the Chesapeake Bay: the prey Atlantic menhaden and its two competing predators, the striped bass and the non-native blue catfish. The model also considers the following ecological issues related to these three species: the overfishing of menhaden, the invasiveness of the blue catfish, and the harvesting of blue catfish as a method to control the population. A series of modeling scenarios are considered based on some simplifying assumptions to demonstrate the application of theoretical concepts to actual fisheries in the Chesapeake Bay. Analysis involves elementary skills such as finding the roots of polynomial equations, computing eigenvalues and eigenvectors, and some advanced topics such as Routh-Hurwitz criteria and the Hartman-Grobman Theorem. Numerical simulations via MATLAB are utilized to produce graphical simulations and analyze long-time behaviors. Our model predicts that if no serious measures are taken to prevent the spread of the invasive blue catfish, the native predator species will be seriously affected and may even become extinct. The model also shows that linear harvesting is sufficient to limit the growth of the invasive catfish population; however, it is not sufficient to save the striped bass from becoming extinct. The results of this study illustrate the fundamental ecological principle of competitive exclusion, according to which two competing species that attempt to occupy the same niche in an ecosystem cannot co-exist indefinitely and one of the two populations will either go extinct or will adapt to fill a different niche.

Impacts of Nonlinear Energy Harvesting and Residual Self-Interference on the Performance of Full-Duplex Decode-and-Forward Relay System

In this paper, we investigate the usage of a nonlinear energy harvester at a full-duplex (FD) relay, which can harvest the energy from radio frequency (RF) signals transmitted from the source. We mathematically derive the exact closed-form expressions of outage probability (OP), throughput, and average symbol error rate (ASER) of the nonlinear energy harvester-wireless information and power transfer-FD relaying (N-WIPT-FDR) system over Rayleigh fading channels. Unlike linear energy harvester, nonlinear energy harvester results in more computational complexity. Furthermore, it makes the outage floor happen faster even when self-interference cancellation (SIC) techniques are effectively applied due to the saturation power threshold of the nonlinear energy harvester. The combination of nonlinear energy harvester characteristic and residual self-interference (RSI) has significant impacts on the OP, throughput, and ASER of the considered N-WIPT-FDR system. On the other hand, there is an optimal energy harvesting (EH) time duration, which minimizes the OP. This optimal value depends on the transmission power of the source and the saturation power threshold of the nonlinear energy harvester. Monte-Carlo simulations are conducted to validate the derived mathematical expressions.

Enhanced modeling of nonlinear restoring force in multi-stable energy harvesters

It is acknowledged that traditional linear piezoelectric cantilever energy harvesters are not effective to extract ambient energy due to the narrow resonant bandwidth and low efficiency. A popular strategy to overcome these disadvantages is applying external magnets to realize multi-stable energy harvesters. Under the external excitation, the inter-well motion occurs between different potential wells in multi-stable energy harvesters, so as to bring out larger displacement and higher voltage output than intra-well motion. The performance of multi-stable energy harvesters has a strong relationship with the nonlinear restoring force, but there is lack of models for accurately describing nonlinear restoring force. This paper proposes a new enhanced model of the nonlinear restoring force to improve the calculating accuracy by taking the influence of rotational angle and axial displacement into consideration. The rotational magnetic charge is presented to calculate the magnetic force exerted by the external magnets. Then, the trajectory method of cantilever beams is employed to reduce the calculation error caused by axial displacement during oscillation. The accuracy of the proposed model for magnetic force calculation along horizontal and vertical directions is verified by the results of numerical simulation. Additionally, experimental results of the nonlinear restoring force for multi-stable energy harvesters show a good agreement with theoretical results. The influence of system parameters on equilibrium points, nonlinear restoring force and dynamic responses of multi-stable energy harvesters has been investigated based on the proposed model.

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.