参数激励下静电驱动MEMS共振传感器的非线性动力特性研究

静电驱动微机电系统(MEMS)共振传感器因其结构简单、应用广泛等优点引起了研究人员广泛的关注,共振传感器件耦合系统在非线性静电力、压膜阻尼、参数激励下呈现出较复杂的非线性振动、不稳定性、分岔与混沌行为.提出参数激励作用下静电驱动微机电系统中梁式微结构共振传感器的动力学模型,采用多尺度方法对微系统的动力学方程进行摄动分析,探讨直流偏置电压、压膜阻尼和交流激励电压幅值对系统频率响应、共振频率的影响规律,结果表明:直流偏置电压和交流电压幅值都具有软化效应,且使共振频率漂移到较小的数值范围,压膜阻尼对共振频率的影响较小,但是增大压膜阻尼会使稳态振幅的峰值明显下降,为静电驱动微机电系统共振传感器的动力学分析与设计提供参考.     

静电悬浮微陀螺的压膜阻尼特性

空气阻尼对静电微陀螺系统的动态特性起着重要的影响。根据流体力学,构建了描述微陀螺内部气体压膜阻尼特性的线性Reynolds方程。将微陀螺内部气膜分成了13个分区,推导了转子在轴向振动、径向振动、径向摆动时的压膜阻尼系数。根据微陀螺的结构参数进行仿真,结果表明:轴向压膜阻尼系数对微陀螺支承系统的动态特性影响最大,而压膜阻尼系数与气体的温度,压强呈线性关系,与振动幅值呈抛物线型关系;在低频段系统呈现阻尼力,而到高频段,系统呈现弹性力。利用Simulink进行了微陀螺的系统建模,得出压膜阻尼系数Cz对PID参数的选取,尤其是Kd参数,起着重要作用,同时对系统的稳定性也有一定的影响。     

斜拉桥塔-索-桥面耦合参数振动模型及响应分析

针对大跨度斜拉桥拉索与桥塔、桥面的协同振动问题,考虑拉索垂度、阻尼、倾角以及重力弦向分力的影响,引入拉索高精度抛物线形,建立了桥塔-索-桥面连续非线性精细化振动模型,推导了桥塔和桥面共同激励作用下斜拉索耦合振动方程,对比分析了2种激振模式下斜拉索的参数振动特性,并编制程序研究了桥面与拉索的频率比、桥面激励幅值、索力及阻尼对结构耦合振动特性的影响规律。结果表明：桥面与拉索频率比对系统振动的影响较大,频率比为1:2和2:1时拉索均产生强烈振动,但2:1激振模式下拉索振幅更大,达到共振时间较长;随着桥面激励幅值的增大,2:1亚谐波共振模式下的拉索振幅增长速率更快;拉索振幅随索力的增大呈非线性减小趋势;斜拉索阻尼超过2%时,继续提高自身阻尼不能有效减小其振动幅值,需要通过设置附加阻尼才能更好地抑制其振动。     

一种微机电非线性耦合系统奇点稳定性研究

工程中许多微机电系统都采用电容驱动原理，这类结构实际上存在着强烈的静电和机械两个物理场的非线性耦合，因此系统的动态特性比较复杂。本文基于一种扭转微镜系统，通过数值分析方法，研究其非线性动态特性，根据理论分析和数值计算证明该系统在相平面中存在两个奇点，一个是稳定中心，一个是鞍点，且两个奇点位置均随施加电压的变化而逐渐靠近，从而得出系统的静态分叉点；同时分析了有阻尼和无阻尼时电压的变化对相轨道的影响，以及阻尼对吸合电压的影响，吸合电压随阻尼的增大而提高，这些研究结果不仅对扭转微镜的设计和应用提供了理论和方法，而且对用电容驱动的微机电系统的设计亦有参考价值。     

斜拉桥塔-索-桥面连续耦合参数振动特性分析

针对端部激励作用下斜拉索与桥塔、桥面协同振动问题,考虑拉索几何非线性、倾角、阻尼以及拉索重力弦向分力的影响,引入拉索高精度抛物线形,建立了桥塔-索-桥面连续非线性精细化振动模型,推导了拉索与桥塔和桥面共同在激励作用下的耦合振动方程组,研究了桥塔-索-桥面结构系统参数的振动特性,并用数值仿真方法分析桥面与拉索频率比、桥面激励幅值、索力及拉索阻尼对结构耦合振动特性的影响规律。结果表明:桥面与拉索的频率比分别为1∶2和2∶1时,拉索会发生不同模式的大幅振动;相比于超谐波共振模式,亚谐波共振模式的拉索振幅更大,但达到共振所需时间较长;拉索振幅随桥面激励幅值的增大呈非线性增大,桥面激励幅值越大,拉索积蓄共振能量所需的时间越短;拉索振幅随索力增大而减小;拉索自身阻尼对其振动的影响较小,增大拉索阻尼时,拉索振幅虽有减小趋势,但是减小幅度有限。     

基于离散单元法的颗粒阻尼耗能减振特性研究

采用离散单元法并从能量耗散的角度研究颗粒阻尼对系统减振特性的影响。建立了颗粒介质细观下的法向、切向和滚动方向的粘弹性接触模型和能量耗散模型,通过冲击激励和简谐激励下系统振动响应的多参数能量耗散分析来研究颗粒阻尼的耗能机理和减振特性。数值试验表明,颗粒介质可以在一个较宽的振动幅值范围内有效的发挥其阻尼效应,其耗能具有阶梯状周期性的特点。填充率是影响颗粒阻尼耗能减振效果的主要工程可控参数并对系统共振频率产生重大影响,当填充率接近极值时,系统出现无阻尼共振及共振频率超出无颗粒系统固有频率的现象。系统在最优填充率下共振时,颗粒与箱体保持恒定相位差的超振幅稳态运动。较小粒径的颗粒可以提高能量耗散率并使振动系统更快趋向静平衡状态,而恢复系数和摩擦系数则对法向和切向耗能的比值有较大影响。     

参数激励下非线性受控系统的动力学和稳定性

研究两自由度参数激励系统的非线性动力学与控制问题．利用Lagrange方程建立含反馈控制的参激捅及其驱动机构组成的系统动力学方程，以多尺度方法获得一阶近似控制方程．然后，对系统受一阶摸态参激主共振与一、二阶模态间3：1内共振联合作用下的幅额响应及其稳定性，以及反馈参数对系统稳态行为的影响作了详细分析．结果表明，响应的稳定域位置和大小取决于位移反馈，位移立方反馈改变了系统的非线性程度，速度反馈类似于阻尼，可使系统呈现自激振动特性．     

基于尺寸效应的FG-SMA微梁非线性自由振动特性研究

形状记忆合金具有相变温度低、输出应力高、能耗小、驱动电压低、可恢复应变大、生物相容性好等特性。随着形状记忆合金制备技术的进一步发展,有学者提出将功能梯度形状记忆合金材料用于微机电系统等智能微结构,将使其具有更优良的特性。因此开展机电多场耦合功能梯度形状记忆合金微结构的非线性自由振动特性研究具有重要研究价值。本文基于冯卡门几何非线性理论,综合考虑静电力和分子间作用力的影响,考虑尺寸效应,基于修正偶应力理论,建立两端固定的功能梯度形状记忆合金微梁模型,对功能梯度形状记忆合金微梁相变前后的机电耦合非线性自由振动问题进行深入研究,分析了尺寸效应参数、几何结构参数和相变参数等对功能梯度形状记忆合金微梁自由振动特性的影响。     

尺度依赖的静电驱动各向异性微板的Pull-in效应

在新修正偶应力理论的基础上建立了一种可用于分析静电驱动各向异性微板的尺度依赖模型。模型中包含有两个材料尺度参数,在考虑材料宏观各向异性的同时也考虑了微观各向异性程度对结构Pull-in特性的影响。通过虚功原理推导了静电驱动微板的非线性控制方程并显式地给出了Pull-in电压和挠度的表达式。算例结果表明:本文模型所预测的Pull-in电压和挠度分别大于和小于经典宏观板理论的预测结果,即反映了微尺度结构下的尺度效应。尺度效应的影响在板厚度与材料尺度参数接近时逐渐增加,而随着两者比值的增加,该影响逐渐减弱,最终可以忽略不计。此外,本文也讨论了初始间隙d对Pull-in电压以及尺度效应的影响。结果表明随着d的增加,Pull-in电压随之增大,而Pull-in挠度变化不大。     

基于尺寸效应的FG-SMA微梁非线性自由振动特性研究

形状记忆合金具有相变温度低、输出应力高、能耗小、驱动电压低、可恢复应变大、生物相容性好等特性。随着形状记忆合金制备技术的进一步发展，有学者提出将功能梯度形状记忆合金材料用于微机电系统等智能微结构，将使其具有更优良的特性。因此开展机电多场耦合功能梯度形状记忆合金微结构的非线性自由振动特性研究具有重要研究价值。本文基于冯卡门几何非线性理论，综合考虑静电力和分子间作用力的影响，考虑尺寸效应，基于修正偶应力理论，建立两端固定的功能梯度形状记忆合金微梁模型，对功能梯度形状记忆合金微梁相变前后的机电耦合非线性自由振动问题进行深入研究，分析了尺寸效应参数、几何结构参数和相变参数等对功能梯度形状记忆合金微梁自由振动特性的影响。     

单自由度参数振动系统非线性响应的若干特征

用数值积分方法，分析了无阻尼单自由度参数振动系统在给定的单频刚度激励和单频外载荷激振时的非线性动力学响应特性。研究表明了参数振动问题的主要特征：1)单频激励多频响应；2)多频响应中各谐波的分布具有特殊的规律；3)系统具有多频共振特性。     

Stochastically Perturbed Linear Gyroscopic Systems

ABSTRACT

Dynamic stability of linear conservative gyroscopic systems under stochastic parametric excitations of small intensity is examined. Conditions for mean square stability of dynamic response are obtained. Results are shown to depend only on those values of the excitation spectral density near twice the natural frequencies and the combination frequencies of the system. These results are applied to the problem of flow induced vibration in a supported pipe conveying fluid with pulsating velocity. The effects of mean flow velocity and virtual mass on the extent of parametric instability regions are then discussed.     

Stability and response of a nonlinear coupled pitch-roll ship model under parametric and harmonic excitations

The present study deals with the response of a two-degree-of-freedom (2DOF) system with quadratic coupling under parametric and harmonic excitations. The method of multiple scale perturbation technique is applied to solve the nonlinear differential equations and obtain approximate solutions up to and including the second order approximations. All resonance cases are extracted and investigated. Stability of the system is studied using frequency response equations and phase-plane method. Numerical solutions are carried out and the results are presented graphically and discussed. The effects of the different parameters on both response and stability of the system are investigated. The reported results are compared to the available published work.     

Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom

In this paper, research on nonlinear dynamic behavior of a string-beam coupled system subjected to parametric and external excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam coupled system. The Galerkin's method is employed to simplify the governing equations to a set of ordinary differential equations with two degrees-of-freedom. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric resonance for the beam, and primary resonance for the string is considered. The method of multiple scales is utilized to analyze the nonlinear responses of the string-beam coupled system. Based on the averaged equation obtained here, the techniques of phase portrait, waveform, and Poincare map are applied to analyze the periodic and chaotic motions. It is found from numerical simulations that there are obvious jumping phenomena in the resonant response–frequency curves. It is indicated from the phase portrait and Poincare map that period-4, period-2, and periodic solutions and chaotic motions occur in the transverse nonlinear vibrations of the string-beam coupled system under certain conditions. An erratum to this article is available at .     

TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURE WITH FUNDAMENTAL FREQUENCY AND FREQUENCY DOMAIN DYNAMIC RESPONSE CONSTRAINTS

In this paper, adaptive genetic algorithm (AGA) is applied to topology optimization of truss structure with frequency domain excitations. The optimization constraints include fundamental frequency, displacement responses under force excitations and acceleration responses under foundation acceleration excitations. The roulette wheel selection operator, adaptive crossover and mutation operators are used as genetic operators. Some heuristic strategies are put forward to direct the deletion of the extra bars and nodes on truss structures. Three examples demonstrate that the proposed method can yield the optimum structure form and the lightest weight of the given ground structure while satisfying dynamic response constraints.     

On statistical quasi-linearization

In carrying out the statistical linearization procedure to a non-linear system subjected to an external random excitation, a Gaussian probability distribution is assumed for the system response. If the random excitation is non-Gaussian, however, the procedure may lead to a large error since the response of bother the original non-linear system and the replacement linear system are not Gaussian distributed. It is found that in some cases such a system can be transformed to one under parametric excitations of Gaussian white noises. Then the quasi-linearization procedure, proposed originally for non-linear systems under both external and parametric excitations of Gaussian white noises, can be applied to these cases. In the procedure, exact statistical moments of the replacing quasi-linear system are used to calculate the linearization parameters. Since the assumption of a Gaussian probability distribution is avoided, the accuracy of the approximation method is improved. The approach is applied to non-linear systems under two types of non-Gaussian excitations: randomized sinusoidal process and polynomials of a filtered process. Numerical examples are investigated, and the calculated results show that the proposed method has higher accuracy than the conventional linearization, as compared with the results obtained from Monte Carlo simulations.     

Nonlinear dynamics of a viscoelastic beam traveling with pulsating speed,variable axial tension under two-frequency parametric excitations and internal resonance

This paper investigates nonlinear combined parametric transverse vibrations of a traveling viscoelastic beam. The combined parametric excitations originate from the time dependency of axial velocity as well as axial tension. Two parametric excitations are enforced into the system amid the internal resonance. Two-frequency parametric resonance is assumed to be comprised of combination parametric resonance of first two modes due to the time dependency of axial velocity, and the principal parametric resonance of first mode due to the variable tension in the axial direction in the presence of internal resonance for viscoelastic beam is considered for the first time. The higher-order integro-partial differential equation of motion is solved through direct method of multiple scales. Continuation algorithm is employed to explore the stability and various bifurcations of the nonlinear dynamic system. Focus has been made to study the effect of variations of fluctuating tension component, fluctuating velocity component independently and when combined, internal and parametric frequency detuning parameters and damping on the system response. Frequency response equilibrium curves are complex and unique in shapes which are embodied with various bifurcations. Such steady-state behavior is not seen in the existent literature. With variation in fluctuating velocity component, the number of steady-state nontrivial equilibrium curves increases to three and with variation in fluctuating axial tension, they become four. In this process, significant changes in stability, number and position of various bifurcations like supercritical and subcritical pitchfork, Hopf and saddle node are observed. Unlike the previous study, the shape, stability and bifurcations of equilibrium curves under the combined effect of axial velocity and tension closely match with the case of fluctuating axial tension component. The effect of variation in internal and parametric frequency detuning parameter is more realized for second mode compared to first mode. A comparison of the present work with a previous one where axial tension is variable reveals many qualitative and quantitative similarities and dissimilarities. But when compared with earlier work where axial velocity is constant, significant dissimilarities are surfaced. The system displays a wide ranging dynamic behavior including stable periodic, quasiperiodic and unstable chaotic behavior. The numerical computation depicts various nonlinear characteristics and oscillatory behaviors which are not found so far in the existent literature.     

Response and stability of strongly non-linear oscillators under wide-band random excitation

A new stochastic averaging procedure for single-degree-of-freedom strongly non-linear oscillators with lightly linear and (or) non-linear dampings subject to weakly external and (or) parametric excitations of wide-band random processes is developed by using the so-called generalized harmonic functions. The procedure is applied to predict the response of Duffing–van der Pol oscillator under both external and parametric excitations of wide-band stationary random processes. The analytical stationary probability density is verified by digital simulation and the factors affecting the accuracy of the procedure are analyzed. The proposed procedure is also applied to study the asymptotic stability in probability and stochastic Hopf bifurcation of Duffing–van der Pol oscillator under parametric excitations of wide-band stationary random processes in both stiffness and damping terms. The stability conditions and bifurcation parameter are simply determined by examining the asymptotic behaviors of averaged square-root of total energy and averaged total energy, respectively, at its boundaries. It is shown that the stability analysis using linearized equation is correct only if the linear stiffness term does not vanish.     

Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations

A stochastic averaging method for strongly nonlinear oscillators with lightly fractional derivative damping of order α (0<α<1) under combined harmonic and white noise external and (or) parametric excitations is proposed and then applied to study the first passage failure of Duffing oscillator with lightly fractional derivative damping of order 1/2 under combined harmonic and white noise excitations in the case of primary parametric resonance. Numerical results show that the proposed method works very well.     

Quasi-Periodic Oscillations,Chaos and Suppression of Chaos in a Nonlinear Oscillator Driven by Parametric and External Excitations

An analysis is given of the dynamic of a one-degree-of-freedom oscillator with quadratic and cubic nonlinearities subjected to parametric and external excitations having incommensurate frequencies. A new method is given for constructing an asymptotic expansion of the quasi-periodic solutions. The generalized averaging method is first applied to reduce the original quasi-periodically driven system to a periodically driven one. This method can be viewed as an adaptation to quasi-periodic systems of the technique developed by Bogolioubov and Mitropolsky for periodically driven ones. To approximate the periodic solutions of the reduced periodically driven system, corresponding to the quasi-periodic solution of the original one, multiple-scale perturbation is applied in a second step. These periodic solutions are obtained by determining the steady-state response of the resulting autonomous amplitude-phase differential system. To study the onset of the chaotic dynamic of the original system, the Melnikov method is applied to the reduced periodically driven one. We also investigate the possibility of achieving a suitable system for the control of chaos by introducing a third harmonic parametric component into the cubic term of the system.