Nonlinear Piezoelectric Vibration Energy Harvester Research Articles

Response analysis of asymmetric monostable energy harvester with an uncertain parameter

The nonlinear piezoelectric vibration energy harvesting system offers a solution to the power supply challenge for low-power sensors. However, In practical engineering, structural parameter uncertainties arise from manufacturing errors, environmental temperature fluctuations, and changes in material properties. Besides, due to inherent flaws in the structure and materials, asymmetry may occur in the potential well, which leads to the complexity of the dynamic behavior exhibited in energy harvesting system. In this paper, in order to investigate the dynamics of the asymmetric monostable piezoelectric energy harvesting system under an uncertain parameter, the orthogonal polynomial approximation method is applied to transform the stochastic system into an equivalent deterministic system. Then, the responses of the equivalent deterministic system are used to reveal the stochastic behavior of the uncertainty system. The results indicate that, when the uncertainty intensity of the cubic nonlinear coefficient is 0, an increase in the asymmetry level of the potential well leads to an increase in the output voltage. Increasing the other parameters, the output voltage is reduced. In addition, as the uncertainty intensity increases, the parameter intervals of chaotic response become wider and the energy harvesting efficiency decreases. Moreover, as the potential well asymmetry increases, the sensitivity of energy harvesting system to uncertain parameter increases.

Frequency Response for Sweep-Up and Sweep-Down of Piezoelectric Energy Harvester

PurposeThe aim of this work is to study the frequency response of linear and nonlinear piezoelectric vibration energy harvester (pVEH) based on Duffing-type nonlinearity and Kirchhoff’s law, and the effect of the effective electromechanical coupling on the frequency response of nonlinear pVEH.MethodsThe analytical technique based on the harmonic balance method (HBM) is used to obtain the mechanical and electrical frequency responses of linear and nonlinear pVEH, and the Jacobian matrix is used to analyze the solutions’ stability. The Runge–Kutta fourth-order method as a numerical technique is used to solve the ordinary differential equations of pVEH.ResultsThe analytical calculations are completed, and the frequency response solution of displacement of pVEH is contained in real and complex values and those of electrical responses are presented. The harmonic balance results are compared with numerical simulations for various hardening nonlinear springs. Simple analytical expressions for the jump points are suggested for the sweep-up and sweep-down frequencies of pVEH.ConclusionsThe analytical analysis shows that the jump-down frequency ratios have definite behaviors for each low and high effective electromechanical coupling of hardening-nonlinear pVEHs. Moreover, the jump-up frequency ratio is directly proportional to the effective electromechanical coupling of hardening nonlinear pVEHs.

Electromechanical model and simple numerical analysis for a piezoelectric vibration energy harvester considering nonlinear piezoelectricity, nonlinear damping, and self-powered synchronized switch circuit

Establishment of an analytical technique that considers nonlinear piezoelectricity, nonlinear damping, and the connections to the self-powered synchronized switch circuit represents a challenging but practical issue in the development of piezoelectric vibration energy harvesters. The two-way coupled analysis method, which combines numerical software with a circuit simulator, can simulate the performance of the harvester, but it imposes a high computational load. We develop a numerical analysis technique that is more readily implemented to allow us to produce accurate predictions of the output power, displacement, and frequency response characteristics of this harvester with the switch circuit. First, we derive the electromechanical equation required for the miniature harvester, and we then determine the parameters in this equation using the harmonic balance method. Finally, the governing equation coupling the piezoelectric vibration energy harvester with the self-powered synchronized switch circuit is simplified, taking the form of a quartic equation with respect to the displacement. The simulation replicated a reduction in the displacement at higher resistive loads, wider variations in the resonance frequency, and the nonlinear stiffness softening characteristics that were observed experimentally. This paper provides a practical method for predicting the performance of the nonlinear piezoelectric vibration energy harvester with the synchronized switch circuit.

Nonlinear arbitrary-directional broadband piezoelectric vibration energy harvester using 3-DOF parallel mechanism

Overcoming the disadvantages of direction selectivity and narrow bandwidth are two key problems to improve the efficiency of energy harvesting from ambient vibration, and also the premises of the practical application of the piezoelectric vibration energy harvester. In this paper, utilizing a 3-DOF parallel mechanism and nonlinear magnetic forces generated by polar opposing magnets, a nonlinear piezoelectric vibration energy harvester is proposed and explored. The kinematic equation, the governing equation of motion, and the piezoelectric coupling equation of the vibration energy harvester are established. On this basis, through numerical simulation, the normal modes of the vibration energy harvester in linear case are explored, the effect of the polar opposing magnets and the nonlinear characteristics are analyzed, the 8 potential wells in three-dimensional space of the vibration energy harvester are investigated, and the motion trajectories of the octuplet stable system are estimated. Then, the developed vibration energy harvester is tested with vibration excitation along different directions and sweep excitations. The results show that the developed vibration energy harvester can harvest vibration energy along any directions, and its bandwidth is extended by introducing magnets. The maximum average power of the developed vibration energy harvester is 22.3 mw for 1 g excitation, and the bandwidth is about 5.5 Hz with its center frequency around 11 Hz. This work proves that using parallel mechanism with nonlinearity is a promising solution to realize arbitrary-directional vibration energy harvester with wide bandwidth.

Simulation and experiment on bridge-shaped nonlinear piezoelectric vibration energy harvester

There is abundant of vibration energy in environment. Using piezoelectric energy harvesters to power ultra-low power wireless sensors has become a hot topic in recent years. Most piezoelectric energy harvesters have satisfactory output only at one resonant frequency, while once the external excitation frequency deviates from the resonant frequency, the voltage output will drop significantly. Therefore, this paper proposes a bridge-shaped piezoelectric energy harvester to broaden the frequency band for energy harvesting, and the harvester can adaptively adjust the natural frequency of the system to match the external excitation. Based on the two-dimensional nonlinear Euler–Bernoulli beam hypothesis and the Hamilton principle, the distributed-parameter dynamic model of the nonlinear energy harvesting system is set up. By use of variation operator and nondimensionalization, we derive the dimensionless electromechanical coupling equations. With the harmonic balance method, the approximate equations for calculating voltage amplitude and average power are derived. And then the model is numerically solved and analyzed by considering the influence of excitation frequency, excitation amplitude, mass position and load on the output performance of the bridge-type piezoelectric energy harvester. Finally, various comprehensive experiments are performed to verify the results of simulation, and the dynamic effects of the moving mass on the output characteristics are studied. It can be noted that the moving mass can improve the voltage output of the bridge type energy harvester by changing the resonant frequency of the bridge-type piezoelectric energy harvester and impacting the piezoelectric beam. The proposed vibration energy collection device can adaptively tune the resonant frequency and has practical value in engineering.

Nonlinear piezoelectric vibration energy harvester with frequency-tuned impacting resonators for improving broadband performance at low frequencies

The paper reports on a nonlinear frequency up-converting vibration energy harvester with enhanced broadband performance below 50 Hz, which is attained by leveraging vibro-impact interaction between two high-frequency piezoelectric generators and two low-frequency resonators with commensurate natural frequencies in the 2:1 ratio. Finite element model was implemented to assess the proposed concept by treating the harvester as a vibro-impact coupled piezoelectric-circuit system. The model accommodates multiple mechanical contact pairs defined by nonlinear dissipative Hunt–Crossley contact force formulation. Effective design principles were applied to maximize power output including near-optimal positioning of the neutral plane in the generators and rational adjustment of response settling time. The fabricated proof-of-concept device was tested in different clearance configurations and under varying harmonic excitation conditions to reveal rich nonlinear dynamics behavior. The measured hardening-type power frequency responses were examined to gain better insight into nonlinear resonance characteristics (instability jumps, frequency hysteresis, etc), which determine effectiveness of micro-power generation. It was demonstrated that the proposed dual-resonator energy harvester favorably harnesses nonlinear resonance amplification to deliver larger average power output (up to 37 μW) and useable bandwidth (up to 9.5 Hz) in comparison to the conventional single-resonator counterparts (delivering up to 26 μW and up to 7 Hz, respectively). The maximum normalized power density of the device is 41 μW cm−3 g−2, while volume figure of merit and 3 dB or 1 dB bandwidth-based figures of merit reach 0.18%, 11 μW cm−3 g−2 and 1.5%, respectively. The latter value indicates superior broadband performance of the device. Adoption of mean performance index and coefficient of variation as complementary figures of merit proved to be valuable in identifying device configuration that yields the most effective and stable broadband operation in a targeted frequency range.

Low-cost orbit jump in nonlinear energy harvesters through energy-efficient stiffness modulation

This paper aims at exposing a nonlinear piezoelectric vibration energy harvester which can achieve low-cost orbit jump and therefore improve its energy harvesting capability through energy-efficient transient stiffness modulation using Synchronized Switch Stiffness Control (SSSC) technique. The proposed orbit jump concept is numerically and experimentally studied with a softening harvester. Corresponding experimental results validate the jump orbit concept and confirm the significant enhancement of the harvested energy. While the presented softening Duffing system is used as demonstration example, the proposed approach can be implemented to hardening Duffing oscillator as well.

Nonlinear vibration energy harvester: Design and oscillating stability analyses

Abstract Energy harvesting, as an alternative power source, is being widely discussed thanks to emerging technologies like IoT, Industry 4.0, or WSNs. This paper deals with a piezoelectric Vibration Energy Harvester (VEH) with auxiliary nonlinear magnetic stiffness. The nonlinear stiffness was designed to increase the average output power of the VEH. A mathematical model is presented to provide a simulation tool for further analysis. A novel method based on stabilization power introduced by a feedback controller to analyse the behaviour of nonlinear VEHs is introduced. The aim of this method is to detect the stability of oscillation amplitudes in relation to the excitation frequency. The result of this method is an amplitude-frequency characteristic and a stability margin around the resonance frequency area. This novel method might be used for an arbitrary nonlinear oscillator, especially for electromagnetic and piezoelectric VEHs. The results were verified by a laboratory experiment on a nonlinear piezoelectric VEH.

Nonlinear piezoelectric vibration energy harvesting from a portal frame with two-to-one internal resonance

In the few decades, the study of electro-mechanical systems which are capable to extract energy from an operating system in the environment has been of most importance. In this work, we present the extraction of energy from a simple portal frame structure excited by a harmonic force, where the energy harvesting is computed by using of a nonlinear piezoelectric material. The dynamical response of the system is examined, when there is 2:1 internal resonance between the symmetric and the sway mode, resulting the saturation phenomenon and vibration energy transfer between the symmetric (vertical) mode and the horizontal (sway) mode. An evaluation of the energy available for harvesting, in each of the considered modes, is computed.

Chaotic Dynamics-Based Analysis of Broadband Piezoelectric Vibration Energy Harvesting Enhanced by Using Nonlinearity

Nonlinear magnetic forces are always used to enlarge resonant bandwidth of vibration energy harvesting systems with piezoelectric cantilever beams. However, how to determine properly the distance between two magnets is one of the key engineering problems. In this paper, the Melnikov theory is introduced to overcome it. Firstly, the Melnikov state-space model of the nonlinear piezoelectric vibration energy harvesting (PVEH) system is built. Based on it, chaotic dynamics mechanisms of achieving broadband PVEH by nonlinearity are exposed by potential function of the unperturbed nonlinear PVEH system. Then the corresponding Melnikov function of the nonlinear PVEH system is defined, based on which two Melnikov necessary conditions of determining the distance are obtained. Finally, numerical simulations are done to testify the theoretic results. The results demonstrate that the distance is closely related to the excitation amplitude and frequency once geometric and material parameters are fixed. Under a single-frequency excitation, the nonlinear PVEH system can generate a periodic vibration around a stable point, a large-amplitude vibration around two stable points, or a chaotic vibration. The proposed method is very valuable for optimally designing and utilizing nonlinear broadband PVEH devices in engineering applications.

Homotopy analysis approach for nonlinear piezoelectric vibration energy harvesting

Piezoelectric energy harvesting from a vertical geometrically nonlinear cantilever beam with a tip mass subject to transverse harmonic base excitations is analyzed. One piezoelectric patch is placed on the slender beam to convert the tension and compression into electrical voltage. Applying the homotopy analysis method to the coupled electromechanical governing equations, we derive analytical solutions for the horizontal displacement of the tip mass and consequently the output voltage from the piezoelectric patch. Analytical approximation for the frequency response and phase of the geometrically forced nonlinear vibration system are also obtained. The research aims at a rigorous analytical perspective on a nonlinear problem which has previously been solely investigated by numerical and experimental methods.

Comments on “Non-Linear Piezoelectric Vibration Energy Harvesting From a Vertical Cantilever Beam with Tip Mass”

This paper first points out the retaining higher order terms in the main equation of previous study(PS)of Friswell et al. (Journal of Intelligent Material Systems and Structures 23(13): 1505–1521, 2012). The equations of motion for the system are derived following energy (Lagrange) based approaches and the correct equation with the extra higher order terms is provided and simulations are redone in the current study (CS).

Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass

A common energy harvesting device uses a piezoelectric patch on a cantilever beam with a tip mass. The usual configuration exploits the linear resonance of the system; this works well for harmonic excitation and when the natural frequency is accurately tuned to the excitation frequency. A new configuration is proposed, consisting of a cantilever beam with a tip mass that is mounted vertically and excited in the transverse direction at its base. This device is highly non-linear with two potential wells for large tip masses, when the beam is buckled. The system dynamics may include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. The electromechanical equations of motion for this system are developed, and its response for a range of parameters is investigated using phase portraits and bifurcation diagrams. The model is validated using an experimental device with three different tip masses, representing three interesting cases: a linear system; a low natural frequency, non-buckled beam; and a buckled beam. The most practical configuration seems to be the pre-buckled case, where the proposed system has a low natural frequency, a high level of harvested power and an increased bandwidth over a linear harvester.