面内压电振动能量采集动力学设计与性能研究

压电振动能量采集将环境中普遍存在的机械能转换为电能，可以实现自供能传感、控制与驱动，具备灵活、节能环保、可持续的优势，具有广阔的应用前景。为了促进压电振动能量采集器件的集成与融合，提出面内压电振动能量采集，将压电振动能量采集器进行扁平化设计，使其在二维平面内采集振动能量，在保证较大功率输出下能够显著减小器件所需三维空间。为了提高输出功率与工作频宽，设计了具有双稳态与力放大机制的面内压电振动能量采集器。考虑弯张小变形，通过能量法建立了面内压电振动能量采集器的机电耦合动力学模型。分析了关键设计参数对面内压电振动能量采集器性能的影响。数值仿真了面内压电振动能量采集器在简谐激励下的俘能性能，结果表明，通过合理的设计，面内压电振动能量采集器可以低频、宽频弱激励下有效俘获能量。面内压电振动能量采集设计方法有利于推动便携式、可穿戴式自供能等方面的应用和产业化。     

Hopf bifurcation analysis of reaction–diffusion neural oscillator system with excitatory-to-inhibitory connection and time delay

The active control approach generally requires power input to suppress vibrations of structures, while the conventional passive manner often causes waste of energy after transferring vibrations of the primary structure to the auxiliary system. In this work, an innovative control strategy based on energy harvesting for efficiently suppressing the cross-flow-induced vibrations such as galloping is proposed. The novel design facilitates the harvester of not only alleviating the oscillation of the primary structure but also seizing the transferred vibrational energy. An analytical model for the coupled nonlinear dynamical system is established by utilizing the Euler–Lagrange principle and implementing the Galerkin discretization. The impacts of the electrical load resistance and tip mass of the energy harvester on the coupled frequency, damping, and the onset speed of instability of the coupled multi-mode system are investigated in details. The results show that there exists an optimal load resistance for each tip mass which maximizes the onset speed of galloping. For control purposes, it is found that there is a well-defined tip mass of the energy harvester at which the coupled system has the highest onset speed of instability, and hence, the bluff body has the lowest vibration amplitude for all considered load resistances. However, to efficiently harvest energy and control the bluff body, both the tip mass of the energy harvester and electrical load resistance can be accurately determined.     

A piezoelectric based energy harvester with dynamic magnification: modelling,design and experimental assessment

This work presents a simple and innovative piezoelectric energy harvester, inspired by fractal geometry and intrinsically including dynamic magnification. Energy harvesting from ambient vibrations exploiting piezoelectric materials is an efficient solution for the development of self-sustainable electronic nodes. After an initial design step, the present work investigates the eigenfrequencies of the proposed harvester, both through a simple free vibration analysis model and through a computational modal analysis. The experimental validation performed on a prototype, confirms the accurate frequency response predicted by these models with five eigenfrequencies below 100 Hz. Despite the harvester has piezoelectric transducers only on a symmetric half of the top surface of the lamina, the rate of energy conversion is significant for all the investigated eigenfrequencies. Moreover, by adding a small ballast mass on the structure, it is possible to excite specific eigenfrequencies and thus improving the energy conversion.     

一种具有新型动力放大器压电悬臂梁俘能器计算模型和解析解

为了提高压电振动能量俘获的效率,提出了一种新型的压电悬臂梁俘能器。新的压电俘能器在悬臂梁固定端安装一个新型动力放大器系统,另一端带有一个有限尺寸的质量块。新型动力放大器由平移及转动约束的弹簧-质量块系统组成。考虑有限尺寸质量块的质量分布效应和平移及转动约束的弹簧刚度等结构参数的影响,利用广义Hamilton原理,针对带有新型动力放大器的压电式悬臂梁俘能器,建立了分布参数型运动微分方程,获得了相应的特征函数,分析了自振频率和能量俘获效果。分析结果表明,考虑质量块偏心距和转动惯量可提高能量俘获效率的预测精度;合理选择动力放大器的平移及转动弹簧刚度可提高能量俘获的效率,降低俘能器的共振频率。     

基于人体运动的压电-电磁混合式振动能量采集研究

将人体运动产生的动能转化为可利用的电能为传感器供电一直是能量采研究中的一个热点。如何有效利用人体运动，增强环境适应能力以及提高能量采集性能仍是俘能研究中需要解决的关键问题。本文基于人体运动特性，设计了一种新型的混合式能量采集器，同时具有压电和电磁转化机制。压电俘能是基于压电梁变形产生电能，电磁发电机采用堆叠磁组构型来切割线圈产生电动势。首先建立了混合式能量采集器的动力学理论模型，用来描述输出电压特性，并与实验进行了对比验证。理论与实验研究均表明，混合式俘能器的输出电压在一定激励频率范围内出现两个波峰。通过调节压电梁长度，可以改变峰值大小以及两个峰值间的频段范围。人体运动实验表明，混合式俘能器中可以在短时间内提供较高的电压输出，比如当跑步速度为5km/h时，3s内就可以输出1.1V直流电压驱动传感器工作；跑步时长为30s时，传感器正常工作时常可以达到77s。本文设计的混合式俘能器不仅可以快速供电，还具有较强的续航能力，这为电池充电或传感器供电提供了潜在的应用价值。     

Nanoscale flexoelectric energy harvesting

One of the most tantalizing applications of piezoelectricity is to harvest energy from ambient mechanical vibrations for powering micro and nano devices. However, piezoelectricity is restricted only to certain materials and is severely compromised at high temperatures. In this article, we examine in detail, the possibility of using the phenomenon of flexoelectricity for energy harvesting. The flexoelectric effect is universally present in all dielectrics and exhibits a strong scaling with size. Using a simple beam-based paradigmatical design, we theoretically and computationally examine flexoelectric energy harvesting under harmonic mechanical excitation. We find that the output power density and conversion efficiency increase significantly when the beam thickness reduces from micro to nanoscale and flexoelectricity-based energy harvesting can be a viable alternative to piezoelectrics. Specifically, the conversion efficiency in flexoelectric transduction at sub-micron thickness levels is observed to increase by two orders of magnitude as the thickness is reduced by an order of magnitude. The flexoelectric energy harvester works even for a single layer beam with a symmetric cross section which is not possible in piezoelectric energy harvesting. Our results also pave the way for exploration of high temperature energy harvesting since unlike piezoelectricity, flexoelectricity persists well beyond the Curie temperatures of the high electromechanical coupling ferroelectrics that are often used.     

基于非线性谐振电路的双稳态俘能器的俘能与动力学特性研究

双稳态俘能器可实现宽频和高效的俘能效果.目前的研究主要在双稳态结构中接入单一电阻电路进行俘能.本文将非线性RLC (电阻-电感-电容)谐振电路引入到三弹簧式双稳态结构中,构建两自由度非线性系统,以实现俘能特性的提升.设计永磁体与线圈的构型,获得了非线性机电耦合系数.推导并得到了两自由度非线性俘能器的控制方程.利用谐波平衡法推导得到了系统的电流与位移的频率响应关系.基于雅可比矩阵对解的稳定性进行了判别.将解析解与数值解进行了对比验证.结果表明,在双稳态俘能器中引入非线性二阶谐振电路不仅有利于低频俘能,还可进一步提升俘能响应,拓宽俘能带宽.相同的电路参数下,与线性电路相比非线性电路可通过电流的倍频现象实现结构更低频率的能量俘获.减小谐振电路与双稳态结构共振频率之比,增加基础激励幅值,减小静平衡点之间的距离均可提升俘能器的俘能效果.通过调控谐振电路与双稳态共振频率之比和基础激励幅值等参数,可实现系统单倍周期响应、多倍周期响应及混沌响应之间的切换.     

Vibration energy harvesting from impulsive excitations via a bistable nonlinear attachment

A vibration-based bistable electromagnetic energy harvester coupled to a directly excited primary system is examined numerically. The primary goal of the study is to investigate the potential benefit of the bistable element for harvesting broadband and low-amplitude vibration energy. The considered system consists of a grounded, weakly damped, linear oscillator (LO) coupled to a light-weight, weakly damped oscillator by means of an element which provides both cubic nonlinear and negative linear stiffness components and electromechanical coupling elements. Single and repeated impulses with varying amplitude applied to the LO are the vibration energy sources considered. A thorough sensitivity analysis of the system's key parameters provides design insights for a bistable nonlinear energy harvesting (BNEH) device able to achieve robust harvesting efficiency. This is achieved through the exploitation of three BNEH main dynamical regimes; namely, periodic cross-well, aperiodic (chaotic) cross-well, and in-well oscillations.     

局域共振型声子晶体板缺陷态带隙及其俘能特性研究

设计了一种由圆柱形散射体嵌入环氧树脂基体而组成的周期阵列局域共振型声子晶体板结构, 分析了其平直带区域以及缺陷态的能量集中特性, 并研究了其振动能量采集特性. 首先基于超元胞法结合有限元方法分析了5 $\times$ 5完美声子晶体结构和缺陷态声子晶体结构的能带曲线和能量传输特性; 考虑点缺陷局域共振声子晶体结构的能量集中特性, 利用压电材料代替超元胞中某点的散射体材料引入点缺陷, 分析其振动能量采集特性, 结果表明单个5 $\times$ 5点缺陷超胞结构共振频带较窄; 为提升俘能效率, 提出两种由3个具有不同缺陷态数量和构型的5 $\times$ 5超元胞结构并联而成的5 $\times$ 15声子晶体板结构, 机电耦合特性分析结果表明: 所提出的局域共振型声子晶体板结构克服了单个点缺陷超胞结构缺陷模过少、共振频带过窄的局限性, 拓宽了俘能器的工作频带, 提高了输出电压; 此外, 引入不同的缺陷态数量和构型, 可以进一步拓宽俘能带宽, 实现更好的俘能效果.      

Modeling and analysis of magnetic spring enhanced lever-type electromagnetic energy harvesters

This study presents a novel enhanced monostable lever-type electromagnetic energy harvester (L-EEH). According to the positions of the coil and the lever pivot, four configurations are discussed to realize a better harvesting performance of the L-EEHs. On the basis of establishing the theoretical model of the L-EEH, the corresponding analytical solutions can be obtained by applying the harmonic balance method. The effects of the nonlinear coe-cient, the lever ratio, the mass ratio, and the circuit parameters on the energy harvesting performance of L-EEHs are analyzed and discussed. The numerical and experimental efforts are carried out to verify the theoretical model and the energy harvesting performance. The results demonstrate that the maximum output voltage can be achieved with an appropriate lever ratio. Furthermore, the L-EEH possesses a considerable energy harvesting performance under a smaller lever ratio compared with the other three configurations. The output power can also be improved by adjusting the tip mass of the lever. The proposed L-EEH has a considerable operating bandwidth and an output power, which can reach 146.6 mW under the excitation amplitude of 0.3g.     

面向压电振动能量俘获的电能管理电路综述

随着物联网(internet of things, IoT)技术的高速发展, 传统的电池供电方式已经不能满足其供电需求. 利用压电能量俘获技术将机械能转换为电能, 可为IoT提供持久的电能, 具有广阔的应用前景. 本文在讨论压电振动俘能器的电学特性基础上, 全面总结了面向压电振动俘能器的电能管理电路的最新研究成果. 电能管理电路通常由AC-DC变换和DC-DC开关变换器(包括控制算法)两部分组成, 前者用于将压电振动俘能器输出的交流电转变为直流电, 后者用于提高能量俘获效率. 首先, 针对AC-DC变换, 分析了全桥整流器、电压倍增器、同步开关电感电路和同步开关电容电路的工作原理和优缺点. 接着, 重点讨论了用于压电振动俘能器的典型开关变换器电路, 包括电感式、全电容式和变压器式DC-DC开关变换器以及AC-DC开关变换器, 分析了它们的特点和适用场合. 最后, 针对压电振动俘能器的特点, 分析了实现最大能量俘获的几种典型控制算法, 包括最大功率点跟踪、阻抗匹配和同步电荷提取控制算法. 本文通过对面向压电振动俘能器的电能管理电路的全面分析和综述, 揭示了该领域目前存在的瓶颈问题, 并展望了其未来发展方向, 对压电能量俘获自供电系统的研究和开发具有重要的参考价值.      

Performance enhancement of wing-based piezoaeroelastic energy harvesting through freeplay nonlinearity

We investigate experimentally how controlled freeplay nonlinearity affects harvesting energy from a wing-based piezoaeroelastic energy harvesting system. This system consisits of a rigid airfoil which is supported by a nonlinear torsional spring (freeplay) in the pitch degree of freedom and a linear flexural spring in the plunge degree of freedom. By attaching a piezoelectric material (PSI-5A4E) to the plunge degree of freedom, we can convert aeroelastic vibrations to electrical energy. The focus of this study is placed on the effects of the freeplay nonlinearity gap on the behavior of the harvester in terms of cut-in speed and level of harvested power. Although the freeplay nonlinearity may result in subcritical Hopf bifurcations (catastrophic for real aircrafts), harvesting energy at low wind speeds is beneficial for designing piezoaeroelastic systems. It is demonstrated that increasing the freeplay nonlinearity gap can decrease the cut-in speed through a subcritical instability and gives the possibility to harvest energy at low wind speeds. The results also demonstrate that an optimum value of the load resistance exists, at which the level of the harvested power is maximized.     

COUPLED ANALYSIS FOR THE HARVESTING STRUCTURE AND THE MODULATING CIRCUIT IN A PIEZOELECTRIC BIMORPH ENERGY HARVESTER

The authors analyze a piezoelectric energy harvester as an electro-mechanically coupled system. The energy harvester consists of a piezoelectric bimorph with a concentrated mass attached at one end, called the harvesting structure, an electric circuit for energy storage, and a rectifier that converts the AC output of the harvesting structure into a DC input for the storage circuit. The piezoelectric bimorph is assumed to be driven into flexural vibration by an ambient acoustic source to convert the mechanical energies into electric energies. The analysis indicates that the performance of this harvester, measured by the power density, is characterized by three important non-dimensional parameters, i.e., the non-dimensional inductance of the storage circuit, the non-dimensional aspect ratio （length/thickness） and the non-dimensional end mass of the harvesting structure. The numerical results show that： （1） the power density can be optimized by varying the non-dimensional inductance for each fixed non-dimensional aspect ratio with a fixed non-dimensional end mass; and （2） for a fixed non-dimensional inductance, the power density is maximized if the non-dimensional aspect ratio and the non-dimensional end mass are so chosen that the harvesting structure, consisting of both the piezoelectric bimorph and the end mass attached, resonates at the frequency of the ambient acoustic source.     

Performance improvement of the stochastic-resonance-based tri-stable energy harvester under random rotational vibration

In this paper, the stochastic-resonance-based tri-stable energy harvester (TEH) is proposed to enhance harvesting performance under random rotational vibration. An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered. The stationary probability density function (SPDF) of the harvester is obtained by the improved stochastic averaging. Then, with the adiabatic approximation theory, the analytical expression of signal-to-noise ratio (SNR) for the TEH is deduced to characterize stochastic resonance (SR). To enhance direct current (DC) power delivery from a rotational TEH, the influences of system parameters on SR is discussed. The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system. The TEH has higher harvesting performance under the optimal SR. That is, the optimal parameter combinations can induce optimal SR and maximize harvesting performance. Thus, the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.     

Investigations on the presence of electrical frequency on the characteristics of energy harvesters under base and galloping excitations

The characteristics and performance of piezoelectric energy harvesters concurrently subjected to galloping and base excitations when using a complex electrical circuit are studied. The considered energy harvester is composed of a bilayered cantilever beam with a square cylindrical structure at its tip. Euler–Bernoulli beam theory, nonlinear quasi-steady hypothesis, and Galerkin method are used to develop a reduced order model of this system. The electrical circuitry of the harvester consists of a load resistance, a capacitance, and an inductance. The impacts of the electrical components of the harvester’s circuitry, the wind speed, and the base excitation frequency and acceleration on the broadband characteristics of the harvester, quenching phenomenon, and appearance of new nonlinear behaviors are deeply investigated and discussed. Different methods were used to characterize the new nonlinear phenomena that took place due to mechanical electrical interaction like the power spectrum and time history. When both coupled frequencies of electrical and mechanical types exist and are far from each other, it is shown that the quenching phenomenon is only related to the coupled frequency of mechanical type. It was also proven that this configuration results on high harvested power with low displacement near the electrical frequency. On the other hand, for a well-defined choice of the electrical components, the results show that a broadband configuration of the harvester can be designed. It is also indicated that the quenching phenomenon interacts with the appearance of hysteresis regions that depends on the value of the base acceleration and initial conditions. Moreover, it was shown that the presence of this inductance may result in broadband system harvesting more power from both galloping and base excitation.     

Structural and electrical dynamics of a grating-patterned triboelectric energy harvester with stick–slip oscillation and magnetic bistability

The majority of research work on triboelectric energy harvesting is on material science, manufacturing and electric circuit design. There is a lack of in-depth research into structural dynamics which is crucial for power generation in triboelectric energy harvesting. In this paper, a novel triboelectric energy harvester with a compact structure working in sliding mode is developed, which is in the form of a casing and an oscillator inside. Unlike most sliding-mode harvesters using single-unit films, the proposed harvester utilizes grating-patterned films which are much more efficient. A bistable mechanism consisting of two pairs of magnets is employed for broadening the frequency bandwidth. A theoretical model is established for the harvester, which couples the structural dynamics domain and electrical dynamics domain. This paper presents the first study about the nonlinear structural dynamics of a triboelectric energy harvester with grating-patterned films, which is also the first triboelectric energy harvester integrating grating-patterned films with a bistable magnetic system for power performance enhancement. Theoretical studies are carried out from the perspectives of both structural and electrical dynamics. Surface charge density and segment configuration of the films affect whether the electrostatic force influences the structural dynamics, which can be neglected under a low surface charge density. Differences in structural response and electrical output are found between a velocity-dependent model and Coulomb’s model for modelling the friction in the triboelectric energy harvesting system. The bistable mechanism can effectively improve the output voltage under low-frequency excitations. Additionally, the output voltage can also be obviously enhanced through increasing the number of the hollowed-out units of the grating-patterned films, which also results in a slight decrease in the optimal load resistance of the harvester. These findings enable innovative designs for triboelectric energy harvesters and provide fabrication guidelines in practical applications.

     

Transverse motions of a single sphere in hanging or swing configurations under a longitudinal flow

As a result of the reporting of casual observations of the oscillation or rotation of the beacons in transmission line guard cables, some attention has been paid to the stability of the guard cables with beacons.The relatively more frequent observation of these motions has been explained in recent papers dealing with the elastic part of the problem as a consequence of the increasing number of resonant frequencies (one for each additional beacon) that can be excited by appropriate aerodynamic loads. But a model that could explain the aerodynamic forces that can give rise to this motion is still lacking.In this paper we consider the transverse motions of a single sphere in two simplified configurations, (1) hanging (tethered at one point), and (2) swing (tethered at two points) under a longitudinal flow, performing small amplitude swinging oscillations or circular-orbit autorotation about an axis parallel to the main flow direction. The dynamic model here presented is based on the motion equations, which also include a model for the aerodynamic lift and drag forces on the sphere in transverse motion, which considers the effect of changes of flow around the sphere due to the cable interference. These forces are contained in the symmetry plane of the flow relative to the sphere, and, when projected on the lateral direction, give rise to a lateral force, which can explain the existence of the azimuthal motion even at a large reduced velocity, outside the vortex induced vibration (VIV) range The conditions for stable small oscillation motion and circular-orbit autorotation of a sphere in a swing configuration are given.The results for the aerodynamic loads in transverse motion have also been applied to the case of a circular-orbit autorotation of a hanging sphere (spherical pendulum) under a vertical flow. The angular rotation speed and the orbit radius (or cable angle) have been determined as a function of aerodynamic coefficients and configuration parameters.     

逆压电效应对双稳态压电俘能器的性能影响研究

为了研究逆压电效应对压电俘能效果的具体影响,本文首先分析了双稳态压电俘能器的分布参数型能量表达式,然后应用广义Hamilton变分原理推导了该俘能系统的动力学方程,最后采用谐波平衡法获得了动力响应解析解。通过对比不同激励频率下的数值仿真结果,讨论了逆压电效应对俘能系统动力响应的影响规律。结果表明,逆压电效应在不同工况下对俘能效果的影响并非单纯起抑制作用,在一定激励强度的高频激励下,逆压电效应对俘能效果的影响起增强作用;弱强度激励下的俘能效果则全程受到抑制作用。     

曲梁压电俘能器强迫振动的格林函数解

本文运用格林函数法求解了曲梁压电俘能器在强迫振动下的解析解.运用微分法分析了压电层合曲梁结构面内各内力,根据曲梁压电 俘能器的动力学方程组,基于压电本构关系,建立了包含径向阻尼但不考虑俘能器曲梁结构部分的轴向力以及轴向惯性项的Prescott力 电耦合模型. 采用Laplace变换法求得了耦合振动方程的格林函数解.根据叠加原理和格林函数的物理意义,对耦合的系统方程解耦进而 求得强迫振动下曲梁压电俘能器的输出电压. 数值计算中,通过与现有文献的解析解进行对比,验证了本文解析解的有效性,并研究了阻 尼、电阻等重要物理参数对压电函数和谐振频率的影响.通过与有关传统直梁压电俘能器研究成果的对比,体现了曲梁压 电俘能器Prescott模型的高效集能特性. 数值分析研究表明:(1)使得曲梁俘能器达到最大输出电压时连接的最优负载电 阻为1 M$\Omega$;(2)通过更换适当的基底材料,降低材料的弹性模量,可以改变曲梁俘能器的高基频现象,以使结构适应 更复杂的工作环境,但这会导致俘能器的工作效率降低.      

附磁阶梯变厚度悬臂梁压电俘能器的理论建模及分析

论文建立了一种附磁阶梯变厚度压电悬臂梁的动力学模型并分析了系统的俘能特性。基于Euler-Bernoulli梁理论分段建立系统能量函数并引入非线性磁势能，利用Lagrange方程建立了系统机电耦合动力学方程；利用数值方法分析了磁间距对系统振动特性的影响，此外还研究了系统单稳态和双稳态响应，探讨了厚度比、长度比、磁间距和外激励幅值对系统动力学响应和俘能特性的影响。结果表明，磁间距是影响系统势能的主要因素，调节磁间距可使系统产生单稳态和双稳态响应，从而有效提高俘能器俘能特性；与传统等截面悬臂梁压电俘能器相比，通过优化结构参数，附磁阶梯变厚度悬臂梁压电俘能器能够发生明显的非线性振动现象，实现宽频带振动能量采集。