Snap-through piezoelectric energy harvesting

Snap-through mechanism is employed to harvest electricity from random vibration through piezoelectricity. The random excitation is assumed to be Gaussian white noise. The snap-through piezoelectric energy harvester possesses the bistability. For small-amplitude vibration in a potential well, the Ito stochastic differential equation of the electromechanical coupling system is derived from the Taylor approximation at a stable equilibrium point. The method of the moment differential equations is applied to determine the statistical moments of the displacement response and the output voltage. The effects of the system parameters on the output voltage and the output power are examined. The approximate analytical outcomes are qualitatively and quantitatively supported by the numerical simulations. For large-amplitude interwell motion, the effects of the parameters on the output voltage and the output power are numerically investigated. Nonlinearity produced by the snap-through improves energy harvesting so that the snap-through piezoelectric energy harvester can outperform the linear energy harvester in the similar size under Gaussian white noise excitations.     

带碰撞双稳态压电俘能系统的俘能特性研究

双稳态俘能系统的运动常常会陷入单个势能阱中, 导致俘能效率降低. 为了解决这个问题, 本文提出了一类带碰撞的磁斥力双稳态压电振动能量采集系统. 建立了该碰撞双稳态系统的机电耦合方程, 分析了碰撞对双稳态系统动力学特性的影响. 研究了确定性激励和低强度随机激励下碰撞对系统响应特性和俘能效率的影响. 结果表明: 简谐激励下, 碰撞能够使得原双稳态系统的单阱小幅周期运动转变为双阱间的大幅运动, 从而有效地提高输出功率. 得到了低强度随机激励下, 不同碰撞间隙对系统动力响应特性和输出功率的影响规律. 对一个给定的随机激励, 存在一个最优的碰撞间隙, 此时碰撞能够将原双稳态系统单阱内的随机运动转化为频繁的双阱跳跃, 出现大幅值运动, 从而大幅提高了系统的俘能效率.     

Damping as a result of piezoelectric energy harvesting

Systems that harvest or scavenge energy from their environments are of considerable interest for use in remote power supplies. A class of such systems exploits the motion or deformation associated with vibration, converting the mechanical energy to electrical, and storing it for later use; some of these systems use piezoelectric materials for the direct conversion of strain energy to electrical energy. The removal of mechanical energy from a vibrating structure necessarily results in damping. This research addresses the damping associated with a piezoelectric energy harvesting system that consists of a full-bridge rectifier, a filter capacitor, a switching DC–DC step-down converter, and a battery. Under conditions of harmonic forcing, the effective modal loss factor depends on: (1) the electromechanical coupling coefficient of the piezoelectric system; and (2) the ratio of the rectifier output voltage during operation to its maximum open-circuit value. When the DC–DC converter is maximizing power flow to the battery, this voltage ratio is very nearly 1/2, and the loss factor depends only on the coupling coefficient. Experiments on a base-driven piezoelectric cantilever, having a system coupling coefficient of 26%, yielded an effective loss factor for the fundamental vibration mode of 2.2%, in excellent agreement with theory.     

Designing and manufacturing a piezoelectric tile for harvesting energy from footsteps

The objective of this research is to design a piezoelectric tile for harvesting energy from footsteps and to optimize the system for harvesting maximum energy. Because piezoelectric modules easily break when directly subjected to energy generated by human movements, we designed a tile that employs indirect energy transmission using springs and a tip mass. We aimed at matching the mechanical resonance frequency of the tile with that of the piezoelectric modules. The resonance frequency of a piezoelectric module with a 10-g tip mass was almost similar to the vibration frequency of the tile at 22.5 Hz when we dropped an 80-g steel ball from a 1-m height. We performed impedance matching and realized a matching value of 15 kΩ. Under these optimal mechanical and electrical conditions, we harvested 770-μW RMS and 55-mW peak output power.     

弹性支撑双稳压电悬臂梁振动响应及能量采集研究

在分析了常规刚性支撑非线性能量采集系统的研究基础上,提出外部磁铁弹性支撑的结构设想,保证系统在低强度激励条件下也能处于双稳态振荡,提高机电能量转换效率.研究表明,对于强度变化的随机激励历程,弹性支撑非线性能量采集系统不需要实时调整磁铁间距,能够更好地迎合强度时刻变化的随机激励源,实现高效的机电能量转换.     

非线性磁式压电振动能量采集系统建模与分析

为便于评价、优化磁式压电振动能量采集系统的性能,系统研究了该类系统的建模与分析方法,建立了非线性的分布参数模型用于描述系统的非线性动力学行为,并采用谐波平衡法给出了谐波响应的解析解.随后利用仿真模型分析了磁铁间距、加速度幅值、负载阻抗对输出功率的影响,比较了不同激励频率和加速度幅值下的最优阻抗.结果表明:双稳态特性适用于低强度的振动环境,且愈接近临界区域,输出功率愈高,而单稳态渐硬特性适用于高强度振动环境,其最优间距并不靠近临界区域;阱间大幅运动和阱内小幅运动均存在高低能量态共存的现象,愈接近临界区域,现象愈明显;激振频率是影响最优负载阻抗的决定性因素.     

随机激励下双稳态压电俘能系统的相干共振及实验验证

随着压电晶体材料的迅速发展, 基于压电效应的能量采集系统是俘获环境中的宽带随机振动能量的一种有效途径. 研究了有限宽带随机激励作用下, 磁斥力双稳态压电俘能系统的相干共振俘能机理, 并进行了实验验证. 运用Euler-Maruyama方法求解了随机非线性压电振动耦合方程, 比较分析了相干共振发生前后系统的动力学特性和俘能效率, 然后基于Kramers逃逸速率解释了相干共振. 最后的随机振动实验结果验证了双稳态压电俘能系统的相干共振俘能机理. 并且观察到: 当相干共振发生时, 系统会在两个势能阱之间剧烈运动, 此时宽带随机振动能量会被转化为大幅值窄带低频振动响应, 从而极大地提高了宽带随机振动能量的俘获效率.     

Nonlinear dynamics for broadband energy harvesting: Investigation of a bistable piezoelectric inertial generator

Vibration energy harvesting research has largely focused on linear electromechanical devices excited at resonance. Considering that most realistic vibration environments are more accurately described as either stochastic, multi-frequency, time varying, or some combination thereof, narrowband linear systems are fated to be highly inefficient under these conditions. Nonlinear systems, on the other hand, are capable of responding over a broad frequency range; suggesting an intrinsic suitability for efficient performance in realistic vibration environments. Since a number of nonlinear dynamical responses emerge from dissipative systems undergoing a homoclinic saddle-point bifurcation, we validate this concept with a bistable inertial oscillator comprised of permanent magnets and a piezoelectric cantilever beam. The system is analytically modeled, numerically simulated, and experimentally realized to demonstrate enhanced capabilities and new challenges. In addition, a bifurcation parameter within the design is examined as either a fixed or an adaptable tuning mechanism for enhanced sensitivity to ambient excitation.     

Nonlinear optimization of acoustic energy harvesting using piezoelectric devices

In the first part of the paper, a single degree-of-freedom model of a vibrating membrane with piezoelectric inserts is introduced and is initially applied to the case when a plane wave is incident with frequency close to one of the resonance frequencies. The model is a prototype of a device which converts ambient acoustical energy to electrical energy with the use of piezoelectric devices. The paper then proposes an enhancement of the energy harvesting process using a nonlinear processing of the output voltage of piezoelectric actuators, and suggests that this improves the energy conversion and reduces the sensitivity to frequency drifts. A theoretical discussion is given for the electrical power that can be expected making use of various models. This and supporting experimental results suggest that a nonlinear optimization approach allows a gain of up to 10 in harvested energy and a doubling of the bandwidth. A model is introduced in the latter part of the paper for predicting the behavior of the energy-harvesting device with changes in acoustic frequency, this model taking into account the damping effect and the frequency changes introduced by the nonlinear processes in the device.     

Rogue waves in a multistable system

Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.     

Sparse identification method of extracting hybrid energy harvesting system from observed data

Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency. Sometimes, it is difficult to model the governing equations of the hybrid energy harvesting system precisely, especially under external excitation. Accompanied with machine learning, data-driven methods play an important role in discovering the governing equations from massive datasets. Recently, there are many studies of data-driven models done in aspect of ordinary differential equations and stochastic differential equations (SDEs). However, few studies discover the governing equations for the hybrid energy harvesting system under harmonic excitation and Gaussian white noise (GWN). Thus, in this paper, a data-driven approach, with least square and sparse constraint, is devised to discover the governing equations of the systems from observed data. Firstly, the algorithm processing and pseudo code are given. Then, the effectiveness and accuracy of the method are verified by taking two examples with harmonic excitation and GWN, respectively. For harmonic excitation, all coefficients of the system can be simultaneously learned. For GWN, we approximate the drift term and diffusion term by using the Kramers-Moyal formulas, and separately learn the coefficients of the drift term and diffusion term. Cross-validation (CV) and mean-square error (MSE) are utilized to obtain the optimal number of iterations. Finally, the comparisons between true values and learned values are depicted to demonstrate that the approach is well utilized to obtain the governing equations for the hybrid energy harvester under harmonic excitation and GWN.     

Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device

This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free–free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.     

An application of stochastic resonance for energy harvesting in a bistable vibrating system

The application of stochastic resonance to mechanical energy harvesting is currently of topical interest, and this paper concentrates on an analytical and experimental investigation in which stochastic resonance is deliberately exploited within a bistable mechanical system for optimised energy harvesting. The condition for the occurrence of stochastic resonance is defined conventionally by the Kramers rate, and the modelling of a theoretical nonlinear oscillator driven by a small periodic modulating excitation and a harvestable noise source, which, together satisfy this condition, is developed in the paper. A novel experiment is also discussed which validates this particular form of stochastic resonance, showing that the response can indeed be amplified when the frequency of the weak periodic modulating excitation fulfills the correct occurrence condition. The experimental results indicate that the available power generated under this condition of stochastic resonance is noticeably higher than the power that can be collected under other harvesting conditions.     

Dynamic multistable states in a system of magnetic dipoles

Bistable and multistable states induced by a fluctuating magnetic field in a system of four magnetic dipoles were studied numerically. The possibility of performing switchings and cyclic transitions between the different oscillatory regimes by changing field parameters is examined, along with the possibility of creating conditions under which the system is sensitive to noise signals.     

The dynamic characteristics of harvesting energy from mechanical vibration via piezoelectric conversion

As an alternative power solution for low-power devices, harvesting energy from the ambient mechanical vibration has received increasing research interest in recent years. In this paper we study the transient dynamic characteristics of a piezoelectric energy harvesting system including a piezoelectric energy harvester, a bridge rectifier, and a storage capacitor. To accomplish this, this energy harvesting system is modeled, and the charging process of the storage capacitor is investigated by employing the in-phase assumption The results indicate that the charging voltage across the storage capacitor and the gathered power increase gradually as the charging process proceeds, whereas the charging rate slows down over time as the charging voltage approaches to the peak value of the piezoelectric voltage across the piezoelectric materials. In addition, due to the added electrical damping and the change of the system natural frequency when the charging process is initiated, a sudden drop in the vibration amplitude is observed, which in turn affects the charging rate. However, the vibration amplitude begins to increase as the charging process continues, which is caused by the decrease in the electrical damping （i.e., the decrease in the energy removed from the mechanical vibration）. This electromechanical coupling characteristic is also revealed by the variation of the vibration amplitude with the charging voltage.     

Vibration confinement and energy harvesting in flexible structures using collocated absorbers and piezoelectric devices

We propose an optimal design for supplementing flexible structures with a set of absorbers and piezoelectric devices for vibration confinement and energy harvesting. We assume that the original structure is sensitive to vibrations and that the absorbers are the elements where the vibration energy is confined and then harvested by means of piezoelectric devices. The design of the additional mechanical and electrical components is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers and capacitances, load resistances, and electromechanical coupling coefficients are optimized to minimize the total energy of the structure. We use the Galerkin procedure to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers and harvesting devices. We develop a numerical code that determines the unknown parameters of a pre-specified set of absorbers and harvesting components. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To illustrate the proposed design, we consider a simply supported beam with harmonic external excitations. Here, we consider two possible configurations for each of the additional piezoelectric devices, either embedded between the structure and the absorbers or between the ground and absorbers. We present simulations of the harvested power and associated voltage for each pair of collocated absorber and piezoelectric device. The simulated responses of the beam show that its energy is confined and harvested simultaneously.