RLC串联电路与微梁耦合系统的吸合电压与电振荡

根据电阻电感电容RLC电路与微梁耦合系统物理模型,利用拉格朗日-麦克斯韦方程建立了反映RLC电路与微梁机电耦合特征的数学模型。此模型能够反映机电的耦合特征。当两个极板之间的电介质为石蜡、陶瓷、云母等填充物时,只需求解RLC串联电路方程;当电路中放电结束瞬间,电容器极板上电荷为零,此时系统转化为极板微梁振动系统。通过伽辽金方法推导出了极板微梁系统的非线性振动方程,并求得了极板的吸合电压;应用常微分方程理论得到了RLC串联电路方程电振荡的解析表达式,分析了系统的电振荡特性。研究结果表明:对于每一个激励电压值,极板都有两个可能的平衡位置;电路中电流在非共振情况下经过一段时间的振荡后达到稳定。     

索-梁耦合系统解的稳定性分析

研究了在惯性参考系中弹性斜拉索与悬臂梁耦合结构的非线性动力学问题,利用Hamilton原理建立了索-梁耦合系统的非线性动力学方程,利用Galerkin方法将索-梁耦合系统的非线性运动偏微分方程离散为一组常微分方程,然后利用多尺度法分析研究索-梁耦合动力学系统的非线性振动,对耦合系统解的稳定性进行了分析,用Runge-Kutta法对数学模型进行数值计算,并提出对工程有实际意义的结论.     

一类刚-柔耦合系统的建模与稳定性研究

对于由中心刚体带有柔性梁附件组成的这一类简单刚 柔耦合系统，目前文献广泛采用的Ｅｕｌｅｒ Ｂｅｒｎｏｕｌｉ梁模型中考虑的刚 柔运动耦合项有严重的缺陷．本文对于物理本构关系线性的有限变形梁，分别采用微元法和变分法建立了该系统大挠度非线性动力学方程组．本文使用严格的方法来研究此非线性耦合动力学模型，采用能量 动量矩组合方法构成Ｌｉａｐｕｎｏｖ函数，严格证明了此非线性系统平凡解的积分范数稳定性以及具有鲜明物理意义的最大模范数稳定性．本文对文献中引用的三类线性化模型，采用假设模态法，对中心刚体匀速转动时梁的振动作了数值仿真，进一步验证了本文的结论．上述结果，对选择刚 柔耦合系统正确的动力学模型是有益的．     

四边固定加劲板的非线性自由振动

针对工程中常用的加劲板, 研究了非线性振动的求解方法与振动特性. 将加劲板分为板与加劲肋两个部分考虑, 其中板视为考虑几何非线性的大挠度板, 加劲肋视为Euler梁. 假定加劲板的位移, 利用Lagrange方程结合系统能量和振型叠加推导了加劲板的动力平衡方程. 运用椭圆函数及摄动法计算加劲板非线性振动的单模态解, 多模态解则通过增量迭代法进行求解. 最后, 结合有限元软件ANSYS对一个四边固定且不可移动的加劲板进行分析, 讨论解的收敛性, 并分析两个方向设置不同数量加劲肋的情况下非线性自振频率与振幅的关系, 得到了一些加劲板非线性振动特性.      

载流简支微梁在磁场中的磁弹性随机振动

研究了简支微梁在磁场中的随机振动。基于修正的偶应力理论及磁弹性理论建立了外加磁场情况下载流微梁的运动方程,导出了微梁的磁弹性随机振动方程。利用模态分析法分别得到了外加磁场情况下通入平稳和非平稳随机电流时微梁的随机位移响应的均值、功率谱密度函数等数字特征。对通入平稳随机电流的简支微梁进行了算例分析,并绘制了在不同随机电流、磁场强度和本征长度下的位移响应功率谱密度图。计算结果表明,耦合项的存在使得振动响应能量发生了很大的变化,对微梁的疲劳寿命也会产生显著的影响,通过改变随机电流和磁场强度来改变振动能量的分布规律,进而可以达到控制微梁随机振动的目的。     

基于自旋梁的压电振动能量采集与动力学分析

为研究轴向载荷及梁上外激励共同作用下自旋梁结构强迫振动的压电振动能量采集问题,文章提出运用格林函数法求解自旋梁压电俘能器强迫振动下的电压解析解.基于Euler-Bernoulli梁理论,采用扩展Hamilton原理及PZT-5A压电本构,建立了自旋梁压电俘能器强迫振动的力电耦合模型.采用Laplace变换法求得耦合振动方程的格林函数解,并根据线性叠加原理和格林函数的物理意义,对耦合的系统方程进行解耦,进而求得强迫振动下自旋梁压电俘能器的电压解析解.数值计算中,通过与现有文献中的解析解以及实验结果进行对比,验证了本文解的有效性,并分别分析了自旋梁压电俘能器的压电响应与电阻、转速等重要物理参数之间的关系.数值分析研究表明:(1)自旋梁俘能器的压电响应随电阻阻值的增大而增大,直至阻值达到最优负载电阻;(2)通过调高转速,可以提高压电俘能器的最大输出电压;(3)通过降低轴向载荷,可在保持俘能器高效工作的情况下改善俘能器的高基频现象.     

梁的纵向与横向耦合振动的动力学分析

研究了梁发生纵向与横向耦合振动时的非线性动力学行为.从梁的基本方程出发,利用Galerkin截断得到了梁含二次非线性项和三次非线性项的运动微分方程,并通过多尺度法对控制方程进行摄动求解得出了梁纵向模态和横向模态之间产生的内共振.然后对内共振条件下的梁进行了分析和数值模拟,分别讨论了纵向和横向荷载作用下结构的动力学特征.分析表明一定条件下梁存在能量在振动模态间传递的饱和现象,并且某些参数组合下纵向和横向振动之间存在相互耦合的无周期响应现象,从而引起梁结构的大幅振动.     

高度非线性孤立波与Euler梁的耦合作用研究

无预压缩一维颗粒链中的机械撞击以高度非线性孤立波的形式传播,该孤立波是一种能量包,在较长距离内保持稳定波幅。本文研究高度非线性孤立波与Euler梁的耦合作用,对颗粒链采用离散元模型,基于Hertz定律和Euler梁振动方程并考虑Euler梁的横向振动,建立颗粒链与Euler梁耦合的微分方程组。采用Runge-Kutta法进行求解,得到晶体链中各颗粒的位移、速度解。分析回弹波出现的时间、波幅以及Euler梁的材料特性和几何特性参数等对反射孤立波的影响,结果表明,反射孤立波对Euler梁的弹性模量和几何尺寸在一定范围内是敏感的。本文的研究成果丰富和完善了孤立波探伤理论,为一维颗粒链的实际应用提供了广阔的应用前景。     

发电机组转子轴系扭振模化系统的三重共振

建立了发电机组转子轴系扭振模化系统的数学模型，此模型具有平方非线性并受简谐激励作用．研究了系统的固有频率存在双重内共振关系ω３≈２ω２，ω２≈２ω１且Ω≈ω２时的三重共振问题．文中应用非线性振动的改进平均法，求得了系统三重共振的一次近似解，对三重共振的定常解进行了理论分析和数值计算，并进行了奇异性分析，文中指出三重共振解具有双饱和特性，对二种主要的理论分析和数值计算结果进行了实验验证，实验结果与理论结果相符．     

考虑几何非线性的变截面连续梁桥车桥耦合振动分析

将Euler-Bernoulli梁理论与有限分段思想相融合推演出考虑桥梁几何非线性的变截面连续梁桥振动平衡方程;在其与1/4车辆振动方程耦合后,由振型分解法分离变量即可获得车桥耦合振动方程组的时变系数矩阵;借助Runge-Kutta法计算出变截面梁桥任意桥位的振动响应。实例计算结果表明,总体上考虑与忽略桥梁几何非线性的变截面连续梁桥两种情况下车桥耦合振动跨中竖向位移曲线的趋势基本一致;考虑桥梁几何非线性后跨中竖向位移变小,但相差不大,位移响应随车速提高而最大差值增大,且最大偏差点也会出现在除曲线峰值处的其他位置。     

The study on the chaotic motion of a nonlinear dynamic system

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长型浮置板轨道隔振系统理论分析(Ⅰ)——弥散曲线及临界速度

浮置板轨道结构是近年来减振降噪效果最好的轨道结构形式.将整个轨道结构看作一个隔振黑匣子,钢轨与浮置板分别用欧拉梁来模拟,推导动力方程,用傅氏变换将其转换到频率-波数域中,求得系统的弥散方程,并给出轨道结构临界速度计算方法.定义了反映浮置板轨道结构参数的质量比例ξ_(m)、刚度比例ξ_(h)及阻尼比例ξ_(c)等三个系数.在给定实际中板上结构物理参数的条件下,深入讨论了三个比例系数对于系统弥散曲线以及临界速度的影响,进而为浮置板轨道共振频率及临界速度的初步设计提供建议.     

Impact vibration behavior of railway vehicles: a state-of-the-art overview

Excessive vibrations of railway vehicles induced by dynamic impact loadings have a significant impact on train operating safety and stability; however, due to the complexity and diversity of railway lines and service environment, they are extremely difficult to eliminate. A comprehensive overview of recent studies on the impact vibration behavior of railway vehicles was given in this paper. First, the sources of impact excitations were categorized in terms of wheel-rail contact irregularity, aerodynamic loads, and longitudinal impulses by train traction/braking. Then the main research approaches of vehicle impact vibration were briefly introduced in theoretical, experimental, and simulation aspects. Also, the impact vibration response characteristics of railway vehicles were categorized and examined in detail to various impact excitation sources. Finally, some attempts of using the railway vehicle vibration to detect track defects and the possible mitigation measures were outlined.

Graphic abstract

     

Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid

A nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate is presented using the classical plate theory (CPT). The MEE plate material selected is fiber-reinforced \(\hbox {BaTiO}_{3}\)–\(\hbox {CoFe}_{2}\hbox {O}_{4}\) composite, which contains a partial crack at the center. The CPT and the simplified line spring model for crack terms are modified to accommodate the effect of electric and magnetic field rigidities. The analysis considers in-plane forces for the MEE plate, which makes the model nonlinear. The derived governing equation is solved by expressing the transverse displacement in terms of modal coordinates. An approximate solution for forced vibration of cracked MEE plate is also obtained using a perturbation technique. The effect of part-through crack, volume fraction of the composite on the vibration frequencies and structure response is investigated. The frequency response curves presented shows the phenomenon of hard or soft spring. Furthermore, the devised model is extended to the case of cracked MEE plate submerged in fluid. Velocity potential function and Bernoulli’s equation are used to incorporate the inertia effect of surrounding fluid. Both partially and totally submerged plate configurations are considered. The validation of the present results is carried out for intact submerged plate as to the best of the author’s knowledge the literature lacks in results for submerged-cracked plates. New results for cracked MEE plate show that the vibration characteristics are affected by volume fraction, crack length, fluid level and depth of immersion.     

A novel approach for generating multi-direction multi-double-scroll attractors

Attention is focused in this work on quasiperiodic motion of nonlinear systems whose spectrum contains uniformly spaced sideband frequencies with a distance \(\omega _{d}\) apart, around a frequency \(\omega \) with \(\omega \gg \omega _{d}\) and its integer multiples, which are referred to as carrier frequencies. The ratio of the two frequencies \(\omega \) and \(\omega _{d}\) is an irrational number. A new method based on the traditional incremental harmonic balance (IHB) method with multiple timescales, referred to as Lau method, where two timescales, \(\tau _{1}=\omega t\) (a fast timescale) and \(\tau _{2}=\omega _{d}t\) (a slow timescale), are introduced, is presented to analyze quasiperiodic motion of nonlinear systems. An amplitude increment algorithm is adapted to deal with cases where the two frequencies \(\omega \) and \(\omega _{d}\) are    unknown a priori, in order to automatically trace frequency response of quasiperiodic motion of nonlinear systems and accurately calculate all frequency components and their corresponding amplitudes. Results of application of the present IHB method to quasiperiodic free vibration of a hinged–clamped beam with internal resonance between two transverse modes are shown and compared with previously published results with Lau method and those from numerical integration. While differences are noted between results predicted by the present IHB method and Lau method, excellent agreement is achieved between results from the present IHB method and numerical integration even in cases of strongly nonlinear vibration. The present IHB method is also used to analyze quasiperiodic free vibration of high-dimensional models of the hinged–clamped beam.     

The Semigeostrophic Equations Discretized in Reference and Dual Variables

We study the evolution of a system of n particles in . That system is a conservative system with a Hamiltonian of the form , where W ₂ is the Wasserstein distance and μ is a discrete measure concentrated on the set . Typically, μ(0) is a discrete measure approximating an initial L ^∞ density and can be chosen randomly. When d  =  1, our results prove convergence of the discrete system to a variant of the semigeostrophic equations. We obtain that the limiting densities are absolutely continuous with respect to the Lebesgue measure. When converges to a measure concentrated on a special d–dimensional set, we obtain the Vlasov–Monge–Ampère (VMA) system. When, d = 1 the VMA system coincides with the standard Vlasov–Poisson system.     

Modeling and Analog Realization of the Fundamental Linear Fractional Order Differential Equation

This paper provides a rational function approximation of the irrational transfer function of the fundamental linear fra- ctional order differential equation, namely, whose transfer function is given by for 0<m<2. Simple methods, useful in system and control theory, which consists of approximating, for a given frequency band, the transfer function of this fractional order system by a rational function are presented. The impulse and step responses of this system are derived and simple analog circuit which can serve as fundamental analog fractional order system is also obtained. Illustrative examples are presented to show the exactitude and the usefulness of the approximation methods.     

振动台数字控制系统中的多微机并行处理技术

本文在深入分析振动台对数字振动控制系统要求的基础上，提出了在数字振动控制系统中采用多微机主从式并行处理的方法，并阐述了ＰＣ３８６微机分别与ＴＭＳ３２０Ｃ２５信号处理器和Ｚ８０微机系统实现数据通讯的控制策略。     

Using the delayed feedback control and saturation control to suppress the vibration of the dynamical system

In the present paper, the delayed feedback control is applied to suppress or stabilize the vibration of the primary system in a two degree-of-freedom dynamical system with parametrically excited pendulum. The case of a 1:2 internal resonance between pendulum and primary system is studied. The method of multiple scales is applied to obtain second-order approximations of the response of the system. The system stability and bifurcations of equilibrium point of the averaged equations are computed. It is shown that the delayed feedback control can be used to suppress the vibration or stabilize the system when the saturation control is invalid. The vibration of the primary system can be suppressed by the delayed feedback control when the original system is in the single-mode motion. The effect of gain and delay on the vibration suppression is discussed. As the delay varies at a fixed value of the gain, the vibration of the primary system can be suppressed at some values of the delay. The vibration suppression performance of the system is improved at a large value of the gain. The vibration of the primary system could be suppressed about 56% compared with the original system by choosing the appropriate values of gain and delay. The delayed feedback control also can be used to stabilize the system when the original system is unstable. The gain and delay could be chosen as the controlling parameters. Numerical simulation is agreement with the analytical solutions well.     

Integration of a nonlinear energy sink and a piezoelectric energy harvester

A mechanical-piezoelectric system is explored to reduce vibration and to harvest energy. The system consists of a piezoelectric device and a nonlinear energy sink(NES), which is a nonlinear oscillator without linear stiffness. The NES-piezoelectric system is attached to a 2-degree-of-freedom primary system subjected to a shock load. This mechanical-piezoelectric system is investigated based on the concepts of the percentages of energy transition and energy transition measure. The strong target energy transfer occurs for some certain transient excitation amplitude and NES nonlinear stiffness. The plots of wavelet transforms are used to indicate that the nonlinear beats initiate energy transitions between the NES-piezoelectric system and the primary system in the transient vibration, and a 1:1 transient resonance capture occurs between two subsystems.The investigation demonstrates that the integrated NES-piezoelectric mechanism can reduce vibration and harvest some vibration energy.