Effects of anti-symmetric nonlinear viscous damping on the force transmissibility of multi-degree of freedom structures

In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetric viscous damping. The results reveal that an anti-symmetric nonlinear viscous damping can significantly reduce the transmissibility over all resonance regions for MDOF structures while it has almost no effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to overcome the dilemma in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant region but increases the transmissibility over non-resonant regions.     

Reducing force transmissibility in multiple degrees of freedom structures through anti-symmetric nonlinear viscous damping

In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom (MDOF) structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force transmissibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.     

MOTION OF THE DAMPED FOUCAULT PENDULUM

本文建立运动方程,得到了阻尼傅科摆的解析解,并对解的性质进行了一些探究.文中建立的模型是在理想单摆的基础上增加了科里奥利力和与速度成正比的阻尼力.     

Nonlinear damped vibrations of simply-supported rectangular sandwich plates

The nonlinear, forced, damped vibrations of simply-supported rectangular sandwich plates with a viscoelastic core are studied. The general, nonlinear dynamic equations of asymmetrical sandwich plates are derived using the virtual work principle. Damping is taken into account by modelling the viscoelastic core as a Voigt-Kelvin solid. The harmonic balance method is employed for solving the equations of motion. The influence of the thickness of the layers and material properties on the nonlinear response of the plates is studied.     

伴随变阻尼作用的干摩擦下的车辆系统非线性动力学分析

对分段线性阻尼和干摩擦共同作用下的车辆悬挂系统进行了非线性动力学分析研究，阐述了判定系统周期运动稳定性的理论方法；利用数值模拟方法分析了具有不同阻尼参数组合的系统对简谐激励的振动响应，并分析了由干摩擦引起的粘-滑振动行为．结果表明：提高摩擦力对抑制响应有利，但车辆系统在低速下运行时会出现复杂的粘-滑振动，轮轨之间产生较大的瞬时刚性冲击；而通过增加轮对与侧架的弹性悬挂可以有效减弱这种瞬时刚性冲击．     

Study of the effects of cubic nonlinear damping on vibration isolations using Harmonic Balance Method

In the present study, Harmonic Balance Method (HBM) is applied to investigate the performance of passive vibration isolators with cubic nonlinear damping. The results reveal that introducing either cubic nonlinear damping or linear damping could significantly reduce both the displacement transmissibility and the force transmissibility of the isolators over the resonance region. However, at the non-resonance region where frequency is lower than the resonant frequency, both the linear damping and the cubic nonlinear damping have almost no effect on the isolators. At the non-resonance region with higher frequency, increasing the linear damping has almost no effects on the displacement transmissibility but could raise the force transmissibility. In addition, the influence of the cubic nonlinear damping on the isolators is dependent on the type of the disturbing force. If the strength of the disturbing force is constant and independent of the excitation frequency, then the effect of cubic nonlinear damping on both the force and displacement transmissibility would be negligible. But, when the strength of the disturbing force is dependent of the excitation frequency, increasing the cubic nonlinear damping could slightly reduce the relative displacement transmissibility and increase the absolute displacement transmissibility but could significantly increase the force transmissibility. These conclusions are of significant importance in the analysis and design of nonlinear passive vibration isolators.     

飞机机翼损伤的气动模型及故障诊断研究简

为了确保机翼损伤后飞机的飞行安全，提出了一种在线的故障诊断方法. 首先，根据输入输出特性，采用遗忘因子递推最小二乘法对飞机故障后的气动导数进行辨识，建立了机翼损伤故障的数学模型；然后，结合多模型方法和中心差分卡尔曼滤波器（central difference Kalman filter，CDKF）各自的优点，实现对机翼损伤的故障诊断，并采用强跟踪滤波器在线更新CDKF 的采样点，以增强CDKF 的自适应能力. 最后，通过仿真结果验证了本文所提方法的有效性.     

NUMERICAL SIMULATION STUDY ON DYNAMIC RESPONSE UNDER RUDDER CONTROL

针对超声速机动飞行器舵面操纵动态响应问题,开展了相应的算法研究,建立了适用于模拟舵面与弹体相对运动及弹体气动力动态响应的非定常计算方法和局部动态网格变形技术. 以方形弹超声速绕流为例,验证了所提出的定常和非定常计算方法. 对方形弹舵面操纵的3种基本过程(脉冲、阶跃和谐波) 进行了数值模拟,获得了舵面操纵下导弹的俯仰运动对操纵的响应过程. 研究结果表明,快速的舵面操纵过程,甚至会导致导弹的俯仰运动失稳.     

Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.     

MODELING OF NONLINEAR BEHAVIORS OF IMMERSION JOINT

沉管隧道柔性接头的力学性能是其抗震设计的关键准则. 用有限元方法模拟接头的非线性力学性能需要解决接头处材料非线性和接触非线性两个问题. 为简化分析计算,该文采用分段线性化的方法表征接头的材料非线性问题,引进调整因子改进接触算法中的判断条件,处理接头的边界非线性问题. 通过沉管隧道接头的三维精细化建模,研究了沉管隧道接头在拟静力载荷下的响应,获得了接头的轴向等效刚度曲线、抗弯刚度曲线和非线性耦合的剪切特性曲线,进而分析了不同轴向压力对接头剪切特性的影响.     

低渗透裂缝性油气藏非稳态窜流因子研究简

深入分析了常定窜流因子和现有的非稳态因子对于低渗透基质-裂缝窜流的不适应问题,根据对23 个低渗岩心渗流曲线的拟合分析结果,引入了变渗透率系数,并在此基础上推导了非线性扩散方程,也就是低渗透基质-裂缝系统间窜流的控制微分方程;经过无量纲化处理,引入了动边界条件,分别利用积分方法和矩方法导出了非线性扩散方程在前后两个阶段的近似解析解,并在此基础上构建了非稳态窜流因子的表达形式;新的窜流因子可以有效应用于低渗透基质-裂缝系统间的窜流计算,有限元数值模拟的结果验证了新因子在计算非线性非稳态窜流方面的准确性与可靠性.     

Nonlinear coupling of transverse modes of a fixed–fixed microbeam under direct and parametric excitation

Tuning of linear frequency and nonlinear frequency response of microelectromechanical systems is important in order to obtain high operating bandwidth. Linear frequency tuning can be achieved through various mechanisms such as heating and softening due to DC voltage. Nonlinear frequency response is influenced by nonlinear stiffness, quality factor and forcing. In this paper, we present the influence of nonlinear coupling in tuning the nonlinear frequency response of two transverse modes of a fixed–fixed microbeam under the influence of direct and parametric forces near and below the coupling regions. To do the analysis, we use nonlinear equation governing the motion along in-plane and out-of-plane directions. For a given DC and AC forcing, we obtain static and dynamic equations using the Galerkin’s method based on first-mode approximation under the two different resonant conditions. First, we consider one-to-one internal resonance condition in which the linear frequencies of two transverse modes show coupling. Second, we consider the case in which the linear frequencies of two transverse modes are uncoupled. To obtain the nonlinear frequency response under both the conditions, we solve the dynamic equation with the method of multiple scale (MMS). After validating the results obtained using MMS with the numerical simulation of modal equation, we discuss the influence of linear and nonlinear coupling on the frequency response of the in-plane and out-of-plane motion of fixed–fixed beam. We also analyzed the influence of quality factor on the frequency response of the beams near the coupling region. We found that the nonlinear response shows single curve near the coupling region with wider width for low value of quality factor, and it shows two different curves when the quality factor is high. Consequently, we can effectively tune the quality factor and forcing to obtain different types of coupled response of two modes of a fixed–fixed microbeam.

     

精密仪器设备半挂运输列车的振动模态分析

研究了具有牵引悬置装置的精密仪器设备半挂运输列车的振动问题,建立了14 自由度的动力学模型并进行振动模态分析, 在此基础上,计算了某典型半挂运输列车在有阻尼和无阻尼情况下的固有频率和振型.     

HYBRID OPTIMIZATION STRATEGY FOR MOTION PLANNING OF SPACE ROBOT SYSTEM WITH PRISMATIC JOINT

研究了自由漂浮带滑移铰空间机器人非完整运动规划的最优控制问题,提出一种由高斯伪谱法求解可行解与直接打靶法求解最优解相结合的混合优化策略.首先,根据多体系统动力学理论建立空间机器人的动力学模型,给定系统的初始和目标位形,将空间机器人运动规划问题描述成博尔察（Bolza）型最优控制问题;然后,利用高斯伪谱法将最优控制问题离散为非线性规划问题,求解在较少勒让德-高斯（Legendre-Gauss,LG）点时状态变量和控制变量对应的可行解;最后,在LG点处离散控制变量,作为直接打靶法的初值,利用序列二次规划算法求解空间机器人系统的优化运动轨迹和最优控制输入.通过数值仿真,系统优化运动轨迹光滑平稳,最优控制输入也能很好地满足各种约束条件,仿真结果验证了该混合优化策略的鲁棒性和有效性.     

Higher order accuracy analysis of the second-order normal form method

The second-order normal form method has shown its intelligence in handling the weak nonlinear vibration problems, especially the lightly damped nonlinearities. The new technology can directly realize near identify transformation to the differential equation, while the first-order method has to change the differential equation to the first-order form at the very beginning. In order to get a more precise result, a lot of effort has been done to realize it through eliminating unnecessary approximations or reconsidering the influence of the nonlinearity in the subsequent processing. It is easy to conduct a simplified nonlinear transformation to get the first-order motion equation. Here in this paper, we focus on the higher-order accurate terms in the dynamic equation. The Taylor series expansion and the Poincaré expansion of the nonlinearity indicate that there are other resonance terms existing in final dynamic equation. A?general form of expression for higher-order resonance response function has been derived. The results show that the additional resonance terms cannot obviously increase the accuracy of the second-order normal form method; also, it cannot improve much of the predictions of sub and superharmonic responses.     

Mathematical modelling and control of a nonholonomic spherical robot on a variable-slope inclined plane using terminal sliding mode control

In this paper, the three degrees-of-freedom motion of a two-dimensional rectangular liquid tank under wave action is simulated by the boundary element method in time domain. The coupling effects between tank motion and internal sloshing flow are investigated in partially filled conditions. The fourth-order Runge–Kutta method is adopted to update the wave shape and velocity potential on the free surface. The fully nonlinear mutual dependence of the incident wave, tank motion and internal sloshing flow is decoupled through an auxiliary function method, by which the liquid tank acceleration can be obtained directly without knowing the pressure distribution. The corresponding validation of numerical model is carried out and indicates that the accuracy of the present method is satisfactory to evaluate the dynamic responses of tank and sloshing motion. The corresponding response amplitude operators of tank motions for various wave frequencies, amplitudes and filling conditions are obtained, and the nonlinear coupling effects of sloshing flow on the tank responses are analyzed. It is found that the coupling effects have significant influence on sway and roll motion while have little impact on heave motion. The most important coupling effects on roll motion are the split of peak. In addition, due to the nonlinearity of sloshing flow, the roll motion amplitude is not linearly proportional to wave amplitude.     

THERMOELASTIC VIBRATION OF FLUID-CONVEYING MICROTUBES EMBEDDED IN ELASTIC MEDIUMS

研究热环境中被弹性介质包围的微米输流管道的横向振动问题. 根据Hamilton 原理及非线性热弹性理论建立管道横向振动控制方程,并利用复模态法对其进行求解,得到了系统的固有频率和屈曲失稳临界流速,讨论了环境温度和一些重要系统参数对管道振动特性的影响. 研究结果表明:环境温度变化、管道和流体的微尺度效应、管道外径及弹性介质刚度对输流微管道固有频率和临界流速都有很大影响.     

Transitions from Strongly to Weakly Nonlinear Motions of Damped Nonlinear Oscillators

We construct analytical approximations for the transition from strongly nonlinear, early-time oscillations to weakly nonlinear, late-time motions of single degree of freedom, damped, nonlinear oscillators. Two methods are developed. The first relies on (a) derivation of an analytic solution for the initial value problem of an exactly integrable damped system, (b) development of separate early- and late-time approximations to the damped motion using the integrable solution, and (c) patching of the two approximations in the time domain by imposing continuity conditions on the composite solution at the point of matching. The second approach relies on a multiple-scales application of the method of nonsmooth transformations first developed by Pilipchuck, but complemented with a corrected frequency-amplitude relation. This improved relation is obtained by developing two separate frequency-amplitude asymptotic expansions in the frequency-amplitude plane, that are valid for large and small amplitudes, respectively, and then matching them using two-point diagonal Padé approximants. Comparisons between analytical approximations and numerical results validate the two approaches developed     

二自由度结构受迫非线性振动响应的数值计算

本文研究了由飞机尾部简化而成的二自由度结构受迫非线性振动,由于对复杂的运动方程不作进一步简化,方程中含有强非线性耦合项,首先采用数字滤波技术对系统受确定性激励的响应进行了计算;然后在数字模拟计算的基础上用嫁接的ITO积分方法对系统受随机白噪音激励的响应进行了计算。结果表明,ITO积分的综合嫁接方法有更高的计算效率,结果并表明系统的非线性耦合部分对响应有重大影响,是不能加以忽略的,本文的研究为多自由度非线性结构的响应计算提供了有用的思想和方法。     

一类分段光滑非线性平面运动系统响应特性研究

针对由一个线性子系统和一个非线性子系统构成的两自由度非自治分段光滑非线性平面运动系统的响应特性开展了研究. 该分段光滑非线性模型可用来确定对称转子/定子系统的主要碰摩响应, 且在反映非光滑系统典型特性上具有明显的特征:(1) 切换分界面是由两自由度坐标共同决定的一个幅值曲面;(2) 子系统周期解与分界面的擦碰, 不是发生在一个点上, 而是同时发生在解的所有点上;(3) 完整系统未发现由两子系统共同作用而产生的周期解. 因此, 对于该非光滑系统响应特性的研究, 很难直接利用目前有关非光滑系统平衡点和周期解分岔分析的方法. 为此, 尝试了根据子系统的响应特性, 划分出完整系统响应对分界面处切换的敏感区和非敏感区, 并针对非敏感区可由子系统解的特性求得完整系统的响应, 而针对敏感区通过子系统动力学特征的分析有助于解释完整系统响应的生成机制.