有色噪声激励下双稳态电磁式振动能量捕获器动力学特性研究

随着微机电科技的进步,利用环境振动进行系统自供电已经成为目前非线性动力学研究的热点.以附加线性振子的双稳态电磁式振动能量捕获器为研究对象,建立系统的动力学方程,通过数值仿真研究了有色噪声激励作用下双稳态能量捕获系统的动力学行为,分别从有色噪声强度、质量比和调频比3个方面研究了双稳态系统动力学响应,获得了上述参数对双稳态能量捕获系统动力学特性的影响规律,上述研究结果为双稳态电磁式振动能量捕获系统的相关研究提供理论基础.     

势阱深度对双稳态电磁发电系统发电性能的影响研究

电磁式振动能量捕获技术从单稳态系统发展到多稳态系统,拓宽了响应频带,增大了输出电压,能够获得较好的发电性能.以附加线性振子的双稳态电磁式振动能量捕获器为研究对象,主要研究了势阱深度对双稳态系统发电性能的影响,并基于最优发电性能下的势阱深度,研究了双稳态系统结构参数中质量比与调频比对系统发电性能的影响.通过数值仿真结果说明,在外部激励频率为低频时:势阱深度较大时,双稳态系统的振子只能在一个阱内发生小幅振动运动;当势阱深度小到一定程度时,双稳态系统的振子跨过势垒在两个阱间内发生大幅混沌运动或周期运动,其优于小幅振动运动时的平均输出功率.通过数值模拟,得到双稳态系统具有较高的发电性能下的最优质量比、调频比以及阻尼比参数.     

双稳态压电能量获取系统的分岔混沌阈值

建立了双稳态压电能量获取系统动力学模型并且分析了系统的同宿分岔和混沌等非线性动力学行为.根据受压梁的双稳态特性,提出了等效双稳态压电能量获取系统的数学模型.基于Melnikov理论,获得了谐波激励作用下的能量获取系统关于同宿分岔的定性研究方法.通过优化系统参数,得到了发生同宿分岔的阈值曲线.数值结果显示系统在临界阈值处由单阱运动演变为双阱运动,验证了理论分析的有效性.结果表明Melnikov方法可为能量获取系统的参数设计提供有效的理论依据.     

基于非线性能量阱的双频激励非线性系统减振

针对某型民用航空发动机双频带激励特点,建立了单自由度线性振子耦合非线性能量阱（nonlinear energy sink,NES）的动力学模型.根据典型双转子发动机在巡航状态下低、高特征频率比（1∶4.74）,为系统设定双频带简谐外激励.利用四阶Runge-Kutta算法,研究了耦合NES振子时系统的振动抑制特征,并从外激励频率对系统主振子动能、系统总体能量的影响等方面,与未耦合NES系统、耦合线性动力吸振器两种情况下的数值计算结果进行对比分析.研究结果表明NES对双频带外激励具有更好的振动抑制效果,用NES降低航空发动机振动有可行性.     

车路耦合非线性振动高阶Galerkin截断研究

将移动车辆模型化为运动的两自由度质量-弹簧-阻尼系统,道路模型化为立方非线性黏弹性地基上的弹性梁,并将路面不平度设定为简谐函数．通过受力分析,建立车路非线性耦合振动高阶偏微分方程．采用高阶Galerkin截断结合数值方法求解耦合系统的动态响应．首次研究不同截断阶数对车路耦合非线性振动动态响应的影响,确定Galerkin截断研究车路耦合振动的收敛性．研究结果表明,对于软土地基的沥青路面,耦合振动的动态响应,需要150阶以上的截断才能达到收敛效果．并通过高阶收敛的Galerkin截断研究了系统参数对车路耦合非线性振动动态响应的影响.     

海洋立管双模态动力学分岔分析

为研究剪切流作用下顶张力立管的涡激振动响应规律,将立管简化为Euler-Bernoulli梁模型,用van der Pol尾流振子描述流体的作用,建立了立管涡激振动的非线性动力学模型.基于二阶Galerkin模态离散所得常微分方程组,采用谐波平衡法、Poincaré映射方法和Lyapunov指数法分析系统响应特点.研究结果表明:随着流速的增加,系统响应在周期运动和概周期运动间多次转换,其中周期解区域对应系统的涡激共振区;谐波平衡法结果能够较准确地预测涡激共振区周期解的振幅和频率,以及非涡激共振区概周期解的主要频率成分.     

六维系统环形桁架天线的非线性动力学分析

随着科技的发展,大尺度、低重量、易收拢、高精度等特点是未来天线的主要发展方向.环形桁架天线在发射时整体处于收拢状态,升空后按指令有顺序展开,节省了航天器的空间.此外,环形桁架天线可根据需求设计展开口径的大小.所以,环形桁架天线是目前较为理想的天线结构形式.由于自身结构特点以及复杂的空间环境因素,天线在运行时易产生大幅度的非线性振动,严重影响卫星的稳定运行.因此,将环形桁架天线简化成等效圆柱壳模型,并建立其动力学方程.采用理论分析和数值模拟研究了六维系统环形桁架天线的非线性动力学特性.利用规范型理论化简系统方程分析未扰系统和扰动系统的非线性动力学行为,利用能量相位法验证环形桁架天线系统具有Shilnikov型多脉冲混沌运动,利用数值模拟验证理论分析.并通过数值模拟研究了热激励对环形桁架天线系统非线性振动的影响.     

粘弹性运动带动力响应分析

基于Kelvin粘弹性材料本构模型及带运动方程,建立了运动带非线性动力学分析模型.基于该模型和Lie群分析方法推导了匀速运动及简谐运动带线性问题的解析解;基于该非线性模型的数值仿真讨论了运动带材料参数、带稳态运动速度、扰动速度对系统动态响应的影响.结果表明:1)当带匀速运动时,无论系统是线性还是非线性,运动带横向振动"频率"都随着带运动稳态速度增加而减小.2)随着材料粘性增加,系统耗散能力逐渐增强,动态响应逐渐减小.3)当带运动速度简谐波动时,系统动态响应随扰动速度增大而增大.扰动频率对带横向振动影响较大.     

水平振动下桩基的非线性动力学特性

将桩-土系统看成一个嵌入桩基的粘弹性半空间,利用连续介质力学的方法,在空间柱坐标系中建立了非线性桩-土相互作用的数学模型——桩土耦合的非线性边值问题．在频率域内研究了水平振动下桩基的非线性动力学特性,考察了轴力对桩基非线性动力学特性的影响．研究了多种参数对桩基动力学特性的影响,特别是轴力对桩基刚度的影响A·D2结果表明:在轴力作用下桩基可能丧失承载能力．因此,研究桩基水平振动的力学行为时,必须考察轴力的影响．     

微尺度悬臂管颤振的有限维研究

基于修正的偶应力理论并考虑Lagrange应变张量所给出的几何非线性,运用Hamilton原理建立了微尺度悬臂管平面振动的积分-微分方程.通过Galerkin方法将原积分-微分方程离散成常微分方程组,研究了临界流速-质量比曲线的不同阶Galerkin近似解与精确解的符合程度以及它们对材料长度尺寸参数的依赖性.对不同的模态截断数,运用基于中心流形-范式理论的投影法计算了临界流速处系统的第一Lyapunov(李雅谱诺夫)系数和临界特征值关于流速的变化率,以此为基础分析了系统的分岔模式,探讨了模态截断数对系统动力学性质的影响.临界流速-质量比曲线的滞后部分及交点处的动力学性质表明,系统存在不同的分岔方向,用6个模态的Galerkin离散化方程作分岔图对此进行了验证,并通过理论分析及数值方法分别计算了颤振的固有频率.     

磁振子压电能量采集器的多尺度分析

根据磁振子压电能量采集器实验系统的数学模型,基于系统静平衡位形,引入坐标变换,建立相对位移的标准控制方程.利用Taylor级数展开法处理磁力非线性项,运用多尺度法近似解析分析,通过消除长期项获得可解性条件,并由此推导出稳态响应时的幅频关系.四阶Runge-Kutta方法用于数值计算受迫振动时间历程,数值算例给出了系统前两阶主共振下的稳态幅频响应关系及其失稳区域.结果表明多尺度方法所得到的一致有效解具有较高精度,可以为优化设计磁振子压电能量采集器提供理论依据.     

惯容器非线性减振与能量采集一体化模型动力学分析

为了解决航天工程中减振和能源供应的问题，构建了一种应用于航天工程的整星减振和能量采集一体化装置，设计并考察了一种基于非线性能量汇(nonlinear energy sink, NES)的新型非线性减振装置，通过以惯容器(inerter)替代传统的惯性元件以减少负载质量，并在该装置中整合了基于超磁致伸缩材料(giant magnetostrictive material, GMM)的能量采集器.在整星减振的实际背景下对其进行了建模、仿真和分析，同时通过数值计算，考察分析了能量采集器采集振动能量的效果，研究结果表明，在合理选择的参数下，该NES-inerter-GMM(NES-I-GMM)装置能够很好地起到减振作用，同时收集一定的振动能量.     

Modeling and analysis of distributed electromagnetic oscillators for broadband vibration attenuation and concurrent energy harvesting

Many energy harvesting devices employ dynamics ascribed to the classical vibration absorber. Conventional models suggest that when host structural motion excites the harvesters at resonance, maximum electrical power output is achieved. As the harvesters become inertially substantial relative to the structure, this condition no longer holds since the electro-elastic response of the harvester is coupled to the structural vibration. In this regime, the devices become true vibration absorbers that alter the structural oscillations which may consequently affect energy harvesting capability. Distributions of point oscillators have been considered as broadband vibration control treatments making it natural to consider the potential for energy harvesting devices to serve this end. This paper presents an analysis of distributed single- and two-degree-of-freedom, linear electromagnetic oscillators attached to a harmonically excited panel. The coupled Euler–Lagrange equations of motion are solved and the simultaneous goals of vibration attenuation of the host panel and harvested electrical power are computed for several scenarios. It is found that design parameters optimizing the individual goals occur in relative proximity such that small compromises need to be made in order to achieve both ends reasonably well, particularly in regards to the overall mass added to the structure.     

Investigation upon the performance of piezoelectric energy harvester with elastic extensions

Piezoelectric vibration energy harvesters have attracted much attention due to its potential to replace currently popular batteries and to provide an sustainable power sources. Many researchers have proposed ways to increase the performance of piezoelectric energy harvesters like bandwidth, working frequency and output performance. Here in this contribution, we propose the method of using elastic extensions to tune the performance of a piezoelectric energy harvester. Mathematical model of the proposed device is derived and analyzed. Numerical simulations are done to investigate the influences of the derived parameters, like length ratio λ_l, bending stiffness ratio λ_B, and line density ratio λ_m. Results show that the elastic extension does change the motion of the proposed device and help tune the performance of piezoelectric energy harvesters.     

Frequency–energy plots of steady-state solutions for forced and damped systems,and vibration isolation by nonlinear mode localization

We study the structure of the periodic steady-state solutions of forced and damped strongly nonlinear coupled oscillators in the frequency–energy domain by constructing forced and damped frequency – energy plots (FEPs). Specifically, we analyze the steady periodic responses of a two degree-of-freedom system consisting of a grounded forced linear damped oscillator weakly coupled to a strongly nonlinear attachment under condition of 1:1 resonance. By performing complexification/averaging analysis we develop analytical approximations for strongly nonlinear steady-state responses. As an application, we examine vibration isolation of a harmonically forced linear oscillator by transferring and confining the steady-state vibration energy to the weakly coupled strongly nonlinear attachment, thereby drastically reducing its steady-state response. By comparing the nonlinear steady-state response of the linear oscillator to its corresponding frequency response function in the absence of a nonlinear attachment we demonstrate the efficacy of drastic vibration reduction through steady-state nonlinear targeted energy transfer. Hence, our study has practical implications for the effective passive vibration isolation of forced oscillators.     

Optimal Impedance Load of a Bistable Energy Harvester

In this contribution we investigate a bistable energy harvester with regard to its optimal impedance load. A bistable energy harvester exhibits three different types of oscillation: Single-well (about a stable equilibrium), cross-well (between the wells) and inter-well (about the unstable equilibrium). The occurring oscillation type depends, for instance, on the excitation parameters and the initial conditions. It has already been observed ( [1]) that the optimal impedance, which allows to maximize the power output, varies for each oscillation type. In our investigations we complement these findings with analytical and numerical calculations. For our analysis we examine the non-dimensionalized coupled equations of a bistable energy harvester. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of a nonlinear MEMS-based piezoelectric resonator for wideband micro power generation

Micro-scale piezoelectric unimorph beams with attached proof masses are the most prevalent structures in MEMS-based energy harvesters considering micro fabrication and natural frequency limitations. In doubly clamped beams a nonlinear stiffness is observed as a result of midplane stretching effect which leads to amplitude-stiffened Duffing resonance. In this study, a nonlinear model of a doubly clamped piezoelectric micro power generator, taking into account geometric nonlinearities including stretching and large curvatures, is investigated. The governing nonlinear coupled electromechanical partial differential equations of motion are determined by exploiting Hamilton's principle. A semi-analytical approach implementing the perturbation method of multiple scales is used to solve the nonlinear coupled differential equations and analyze the primary and superharmonic resonances. Results indicate that operational bandwidth of the nonlinear harvester is enhanced considerably with respect to linear models. Moreover considerable amount of power is generated due to occurrence of superharmonic resonances. This yields to extraction of energy at subharmonics of the natural frequency which is crucially important in MEMS-based harvesters.