两跨输电线非线性主共振响应分析

研究两跨输电线非线性共振响应问题,应用Hamilton变分原理推导了两跨输电线的振动微分方程以及对应的边界条件。利用Galerkin离散方法和多尺度法,得到了单模态主共振响应。研究结果表明:幅频响应曲线表现出软、硬弹簧性质,随着外激励幅值的增大,输电线系统响应由软弹簧性质向硬弹簧性质转换;系统阻尼减小或外激励幅值增大时,系统幅值个数也随之发生变化,表现出多值和跳跃现象。     

李萨如图形在检测系统中的应用

李萨如图形可以检测两个相同频率信号的相位差．主要论述具有惯性质量、弹簧和阻尼器的二阶加速度测量系统,其动态响应特性的分析方法,如何利用李萨如图形来检测力平衡式加速度传感器的动态特性,即幅频特性和相频特性,从而确定传感器的固有频率ω_n和阻尼比ξ,以此来评定传感器的综合特性．     

DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE VIBRATION ISOLATION SYSTEMS WITH DAMPING CONTROL 1)

研究了一类基于相对速度反馈的含立方刚度的单自由度非线性半主动隔振系统.通过平均法得到了系统分别在基于加速度-相对速度反馈的加速度驱动阻尼控制策略、速度-相对速度反馈的天棚阻尼控制策略和位移-相对速度反馈的地棚阻尼控制策略下主共振响应的近似解析解,并利用数值解验证了近似解析解的准确性.通过 Lyapunov 理论对不同控制策略下系统的稳定性进行了分析,讨论了系统参数对控制效果的影响.分析结果表明,对 3 种基于相对速度反馈的控制策略进行解析研究时,切换条件中的控制参数具有相同的表达式;在抑制共振响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略在低频时的减振效果最好,而基于加速度-相对速度反馈的加速度驱动阻尼控制策略在高频时的减振效果最优;在抑制瞬态响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略的减振效果最好.此类解析研究方法可应用到其他半主动开关控制策略中,为半主动隔振系统的控制策略研究提供了有效的方法和手段.     

一类阻尼控制半主动隔振系统的解析研究

研究了一类基于相对速度反馈的含立方刚度的单自由度非线性半主动隔振系统.通过平均法得到了系统分别在基于加速度-相对速度反馈的加速度驱动阻尼控制策略、速度-相对速度反馈的天棚阻尼控制策略和位移-相对速度反馈的地棚阻尼控制策略下主共振响应的近似解析解,并利用数值解验证了近似解析解的准确性.通过 Lyapunov 理论对不同控制策略下系统的稳定性进行了分析,讨论了系统参数对控制效果的影响.分析结果表明,对 3 种基于相对速度反馈的控制策略进行解析研究时,切换条件中的控制参数具有相同的表达式;在抑制共振响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略在低频时的减振效果最好,而基于加速度-相对速度反馈的加速度驱动阻尼控制策略在高频时的减振效果最优;在抑制瞬态响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略的减振效果最好.此类解析研究方法可应用到其他半主动开关控制策略中,为半主动隔振系统的控制策略研究提供了有效的方法和手段.      

基于多尺度方法的平动圆柱贮箱航天器刚——液耦合动力学研究

以充液航天器为工程背景,借助多尺度方法研究刚--液耦合动力学系统非线性动力学特性.利用多维模态方法,将描述横向外激励下圆柱贮箱中液体非线性晃动的自由边界问题转换为液体模态系数相互耦合的有限维非线性常微分方程组.推导液体晃动产生的作用于贮箱壁的晃动力和晃动力矩的解析表达式,进而建立航天器刚体部分平动和液体晃动耦合的非线性动力学方程组.应用多尺度方法对刚--液耦合系统的动力学特性进行解析分析,通过固有频率的特征方程求解耦合系统固有频率,推导外激励频率接近耦合系统第一阶固有频率时液体晃动稳态解的幅值频率响应方程.结合数值方法,研究了液体晃动稳态解的幅值频率响应曲线和激励--幅值响应曲线.结果表明, 随充液比变化,液体晃动稳态解的幅值频率响应曲线会发生软、硬弹簧特性转换现象和"跳跃"现象;幅值频率响应曲线的软、硬弹簧特性转换点受重力加速度和弹簧刚度系数影响;以上所得研究结果表明,考虑非线性效应时的刚--液耦合系统动力学特性与传统的线性系统模型所显示的动力学特性具有本质区别.本文的研究工作对进一步分析充液航天器刚--液耦合非线性动力学特性具有重要参考价值.      

含分数阶Bingham模型的阻尼减振系统时滞半主动控制

针对基于磁流变液阻尼器的半主动控制系统中存在的时滞问题, 采用了一种将可控的时滞变量引入半主动控制切换条件的控制策略, 研究了考虑时滞的天棚阻尼控制切换条件对半主动阻尼减振系统的影响, 分析了含有分数阶Bingham模型的线性刚度系统在基础激励下的振动特性. 利用平均法得到了系统在含时滞半主动控制策略下主共振响应的近似解析解, 根据Lyapunov理论分析了系统的稳定性. 通过数值解验证了近似解析解的准确性, 二者具有较好的一致性. 利用近似解析解分析了固定激励频率下时滞对系统幅频响应特性的影响, 以及主共振峰值响应和共振频率随时滞变化的特性规律. 结果表明, 含时滞的半主动控制系统存在一个小时滞区间, 使得系统的振幅在主共振峰对应的频率附近低于不考虑时滞时系统的振幅, 且存在最优时滞使得系统的振幅大幅度降低; 而大时滞的引入会加剧系统的振动, 导致系统的颤振. 确定了基于分数阶Bingham模型的线性刚度系统在天棚阻尼半主动控制下的时滞选取原则, 为振动系统半主动阻尼控制中的时滞选取提供了参考.      

Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid

The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourthorder Runge-Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity,interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present, work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender pipes.     

Whirling of a forced cantilevered beam with static deflection. III: Passage through resonance

Nonstationary excitations of slender, elastic, cantilevered beams with equal principal moments of inertia are considered. The excitation frequency is slowly increased or decreased through a resonance of the first mode at a constant rate. Three resonances are investigated: primary resonance, superharmonic resonance of order two and subharmonic resonance of order two. After application of Galerkin's method with three modes, the nonlinear, nonstationary response of the first mode of the beam is determined by two methods: integration of the modulation equations obtained from the method of multiple scales, and direct numerical integration of the temporal equations of motion. Time histories are presented and the effects of excitation amplitude, rate of acceleration or deceleration through resonance, damping and initial conditions of the disturbance on the maximum response are studied. The effect of a persistent random disturbance is also examined. Although the excitation acts in the vertical plane, whirling occurs if the beam is subjected to out-of-plane disturbances.     

Nonlinear dynamic analysis of a quarter vehicle system with external periodic excitation

In this paper, a nonlinear dynamic model of a quarter vehicle with nonlinear spring and damping is established. The dynamic characteristics of the vehicle system with external periodic excitation are theoretically investigated by the incremental harmonic balance method and Newmark method, and the accuracy of the incremental harmonic balance method is verified by comparing with the result of Newmark method. The influences of the damping coefficient, excitation amplitude and excitation frequency on the dynamic responses are analyzed. The results show that the vibration behaviors of the vehicle system can be control by adjusting appropriately system parameters with the damping coefficient, excitation amplitude and excitation frequency. The multi-valued properties, spur-harmonic response and hardening type nonlinear behavior are revealed in the presented amplitude-frequency curves. With the changing parameters, the transformation of chaotic motion, quasi-periodic motion and periodic motion is also observed. The conclusions can provide some available evidences for the design and improvement of the vehicle system.     

分布振子复合板的模态阻尼及多点激励下阻尼减振相关性

分布阻尼振子可拓宽结构减振频带,因此可将振子分布于板中以形成复合板（简称“分布振子复合板”）,进而实现较宽的减振频带．对于多点支撑处受到宽频非一致激励（例如在不同激励点处的激励频率、幅值与相位有差异）的分布振子复合板,目前还缺乏有效简便的优化控制指标．在作者之前的研究中,针对含分布振子的梁推导了基于模态应变能的模态阻尼计算理论,讨论了模态阻尼与单点激励下梁的减振效果的相关性,并应用于宽频减振设计优化．本文进一步将模态阻尼计算理论推广到分布振子复合板,并将研究从梁的单点激励扩展到板的多点非一致激励下的阻尼减振相关性．首先,在利用模态应变能法推导得到分布振子复合板的模态阻尼计算公式后,从理论上讨论了不同边界条件与模态阶次对计算结果的影响,以及计算理论的适用性．而后,进一步通过有限元参数分析了边界条件、频率比、模态阶次与质量比的影响．最后,通过算例分析了无振子板或分布振子复合板在四个激励点具有多种幅值与相位组合情况下的稳态响应．结果表明,推导的模态阻尼计算公式可正确预测不同边界条件下的模态阻尼,且理论预测的模态阻尼与基板的稳态平均加速度减小率、稳态峰值应变能减小率均有较高的相关性．     

时滞耦合质量摆动力吸振器减振系统的等峰优化理论与实验

摆式调谐质量阻尼器因其便于安装、维修、更换,且经济实用,广泛应用于结构减振.它通过将摆的自振频率调谐到接近主系统的控制频率,使摆产生与主系统相反的振动,从而抑制或消除主系统的振动.本文通过对主系统无阻尼的被动减振系统和主系统有阻尼的时滞反馈主动减振系统进行多目标优化设计,实现了对主系统幅频响应曲线的等峰控制和共振峰与反共振峰差值的有效控制.首先,建立了时滞耦合质量摆动力吸振器减振系统的力学模型和振动微分方程,通过对主系统无阻尼的被动减振系统进行等峰优化,获得了减振系统的最优频率比和质量摆的最优阻尼比.对于主系统存在阻尼的被动减振系统,在该优化参数下主系统的幅频响应曲线等峰优化失效.其次,对于主系统存在阻尼的时滞反馈优化控制系统,采用CTCR方法得到了反馈增益系数和时滞的稳定区域.在保证系统稳定的前提下,通过调节反馈增益系数和时滞量两个控制参数能够实现对主系统幅频响应曲线的等峰控制.再次,对共振点处主系统振幅放大因子时滞敏感度和反馈增益系数敏感度进行分析,表明共振点幅值对反馈增益系数比对时滞更为敏感.最后,通过实验分别在频域和时域内对理论结果进行了验证.研究表明,通过采用时滞反馈对摆式调...     

多尺度法的推广及在非线性黏弹性系统的应用

黏弹性材料在航空、机械、土木等领域具有广阔的应用前景,而具有1.5自由度的非线性Zener模型能更好地描述其特性.因此,研究多尺度法的推广和应用具有重要意义.在传统多尺度法的基础上,推广并利用多尺度法对非线性奇数阶微分方程进行研究,解决非线性奇数阶系统的动力学求解问题.以非线性Zener模型为例,首先通过推广的多尺度法...     

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.     

Controlling the vertical shift of an isolated body based on the vibration of nonlinear systems with asymmetric damping forces

Asymmetric damping forces induce the equilibrium position of the isolated body to shift downward. Inspired by this phenomenon, this paper proposes the novel concept of shifting an isolated body based on the vibration of nonlinear systems with asymmetric damping forces. To verify the feasibility of this concept, a piecewise smooth isolation system is established. The incremental harmonic balance method is used to analyze the nonlinear vibration system and to obtain a steady-state analytical solution. The accuracy of the solution is verified by the Runge–Kutta method. Based on the analytical solution, the influences of some key parameters on the system vibration response are analyzed, revealing that the shift in the isolated body height increases with increasing excitation amplitude and damping asymmetry ratio. Additionally, this shift first increases and then decreases with increasing excitation frequency, reaching a peak near the natural frequency of the intermediate body. Finally, considering the complex structure, high energy consumption, and slow response of active suspension actuators, the proposed concept is applied to the tilt control of a vehicle. The simulation results show that the proposed methodology based on this concept can tilt a vehicle body to a certain angle in the turning direction, enabling the use of a semi-active actuator for vehicle tilt control to realize the control effect achieved by an active actuator.

     

弹性屈曲梁在参数激励下的倍周期分叉

考虑一端具有干摩擦的屈曲梁在轴向激励下的非线性振动系统，利用Ｆｌｏｑｕｅｔ理论和谐波平衡法，研究了系统中初始屈曲度、阻尼、频率、激励振幅等各种物理参数对１／２业谐共振情况下倍周期分叉的影响，其规律与以往的数值模拟结果具有很好的一致性。     

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。     

A New Testing Machine for the Dynamic Characterization of High Strength Low Damping Fiber Materials

This work describes a novel method for measuring the damping, the elastic modulus and the non-linear behavior of high strength low damping fiber materials such as para-aramids, silicon carbide (SiC) and carbon. The method is based on resonant response characterization of a spring-mass system excited by a sine-wave forcing term which is applied as a vertical force to the suspended mass. The damping is obtained from the measured resonance quality factor Q, the elasticity modulus is calculated from the resonance frequency, and the non-linear coefficient is obtained with the backbone approach from resonance profile variations as a function of the forcing term amplitude. It is argued that the method is very sensitive, to the point that a maximum excitation amplitude of the order of a few percent of resistance is sufficient to obtain an estimate of the non-linear coefficient. This claim is supported by experimental results. A testing machine is also discussed, which provides the necessary sensitivity at such small excitation amplitudes and the capability of evaluating very small damping values, as expected in high strength low damping fiber materials. The sensitivity is guaranteed by an optical position sensor with sub-micron resolution. To evaluate small damping values, particular care has been taken to ensure that energy dispersions in the generator are much smaller than energy dispersions in the fibers themselves. Examples of dynamic characterization are shown for para-aramid, silicon carbide, and carbon fibers.     

Amplitude reduction of primary resonance of nonlinear oscillator by a dynamic vibration absorber using nonlinear coupling

The paper presents the characteristics of a new type of nonlinear dynamic vibration absorber for a main system subjected to a nonlinear restoring force under primary resonance. The absorber is connected to the main system by a link in order to be excited with twice the frequency of the motion of the main system. The natural frequency of the absorber is tuned to be twice the natural frequency of the main system, in contrast to autoparametric vibration absorber, whose natural frequency is tuned to be one-half the natural frequency of the main system. The presented absorber is not excited through the autoparametric resonance, i.e., no trivial equilibrium state exists. Therefore, the absorber always oscillates because of the motion of the main system and cannot be trapped by Coulomb friction acting on the absorber, in contrast to the autoparametric vibration absorber. Under small excitation amplitude, this absorber does not produce an overhang in the frequency response curve, which occurs because of the use of the conventional autoparametric vibration absorber; the overhang renders the response amplitude larger than that in the case without an absorber. In addition, the absorber removes the hysteresis in the frequency response curve caused by the nonlinearity of the restoring force acting on the main system. Regarding large excitation amplitude, the response amplitude in the main system can be decreased by increasing the damping of the absorber, but that decrease is limited by the nonlinearity in the restoring force acting on the main system. This paper also describes experimental validation of the absorber under small excitation amplitude using a simple apparatus.     

惯容器对隔振系统动态性能影响研究

本文设计了一种滚珠丝杠惯容器及ISD隔振系统,通过实验研究了惯性轮的转动惯量对惯容值的影响;同时,分析了滚珠丝杠惯容器的机械动力学特性,推导了ISD隔振系统的振动传递率计算公式,探讨了惯容器对ISD隔振系统动态特性的影响。在电机被动、主动和混合隔振工况下,开展了弹簧阻尼系统和ISD隔振系统的振动性能对比实验,验证了惯容器对振动系统固有频率和减振效果的影响规律。研究结果表明,惯容器可降低振动系统的固有频率,使共振频率向低频移动,共振振幅降低;在共振频率附近,惯容器可抑制共振振幅,惯容值越高,抑制效果越明显;ISD隔振系统在低频的减振效果优于传统的弹簧阻尼系统;随着频率比的增加,ISD隔振系统的传递率趋于稳定值,惯容器会引起高频隔振性能降低。     

谐波激励下斜拉桥面内非线性振动试验研究

斜拉桥拉索的振动问题一直是桥梁工程领域的研究热点。为揭示拉索大幅振动的力学机理,课题组建立了斜拉桥的全桥精细化模型,本文测试和研究了单频激励下的斜拉桥可能的非线性振动行为。首先,通过自由振动试验测试了模型的模态参数,并与两类有限元模型（OECS模型和MECS模型）进行对比,结果吻合良好。其次,试验研究了在单个竖向简谐激励下斜拉桥模型的非线性响应。研究发现：当激励频率与斜拉桥某阶全局模态频率接近时,主梁产生主共振,并引起多根长索产生大幅的参强振动;当激励频率与某根斜拉索面内一阶频率之比为1：2或者2：1时,可以观测到索中产生超谐波和亚谐波共振现象。