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。     

考虑塔梁影响的斜拉索随机激励参数振动分析

为了揭示随机激励下斜拉索参数振动特性，考虑塔、梁协同振动的影响，建立了高斯白噪声激励下斜拉索-桥塔-桥面梁耦合振动微分方程，推导了耦合体系的伊藤状态方程组，采用Milstein-Platen法构造了斜拉索振动时程求解迭代格式，研究了斜拉索振动的时程、统计和频域特性，分析了桥塔侧向扶正作用、激励强度和索塔梁初始位移对拉索振幅产生的影响．结果表明：随机激励下斜拉索振动呈现出双“拍”振现象，“拍”幅值和周期具有随机性；拉索随机位移均值、均方差在振动初期具有长时间的非平稳特性；拉索响应幅值对应的频率和拉索功率峰值对应的频率基本一致，但随机激励下的拉索幅值和功率峰值更大；拉索振动概率密度曲线满足高斯分布和马尔科夫性质；桥塔侧向扶正作用越强，拉索振幅越小；激励强度越小，拉索振幅越小；各结构初始位移越大，拉索振幅越大，且对桥面梁初始位移越敏感．     

斜拉桥中斜拉索的面内外耦合内共振分析

研究了桥面侧振引起的斜拉索非线性振动问题。基于Hamilton原理建立了拉索的非线性振动控制方程,并利用多尺度法得到了斜拉索振动方程的二阶近似解。通过具体算例分析了斜拉索面内一阶模态与面外一阶模态相互耦合发生内共振的可能性,讨论了拉索倾斜角对拉索振动的影响,比较了在零初始条件和非零初始条件下拉索振动响应的区别。研究发现:拉索内共振发生在一定的激励频率和激励幅值区域内;改变倾斜角度,会影响拉索发生内共振时激励频率区域的大小;初始条件的不同,拉索的振动形式会相差很大。     

不同端部激励下斜拉索的空间耦合振动

斜拉索在端部激励下将发生空间耦合振动.为探究不同端部激励下斜拉索空间耦合振动的特性,利用斜拉索非线性振动运动方程,采用数值方法研究了在第一、二主共振区,上端水平面内激励、下端竖向激励和下端面外激励三种常见情形下斜拉索的空间耦合振动响应.研究表明:因上端水平面内激励和下端竖向激励均是面内激励,对斜拉索空间耦合振动的影响具有相似性;重力的影响使斜拉索面内、外运动方程不同,从而导致斜拉索在面外激励下(下端面外激励)与面内激励下(上端水平面内激励及下端竖向激励)的空间耦合振动特性具有本质区别.     

斜拉索模态试验参数研究

试验模态分析是斜拉桥索力测试中广泛应用的方法。该方法的关键之一是采取合理的试验方案获取可靠的响应信号以识别出正确的索振动频率。本文通过试验,详细讨论了斜拉索模态测试中若干试验参数,如激振类型、激振位置、传感器位置以及频率分辨率对试验结果的影响;比较环境激励与锤击激励的效果,验证了环境激励的方法也可以准确识别索的频率;最后给出了较为合理的斜拉索模态试验方案,用该方案确定的索力与理论计算结果相差不超过 1. 5%。     

端部激励相位差下斜拉索的非线性振动

斜拉桥中拉索承受着多种端部激励，可激发大幅空间振动．以斜拉索为对象，探究不同端部激励间相位差对其非线性振动的影响．首先，推导斜拉索无量纲离散控制方程，引入考虑相位的三向端部激励得到一般化模型；然后，针对拉索下端存在的纵桥向、竖向和横桥向激励的两两组合，受大幅或小幅激励，及其在主共振区或主参数共振区几组因素，共计12种工况，采用数值分析法分别研究了各工况下不同激励相位差时的斜拉索稳态响应．研究发现：激励相位差能加剧与激励频率相近的面内、外模态振动；在任意端部激励组合下，激励相位差不仅可使斜拉索非线性振动出现定量变化，还可改变内共振的表现形式．面内、外激励组合下，相位差对拉索响应幅值的影响以π为周期变化，且当相位差趋于π/2 + kπ (k = 0, 1, 2…)时影响最为突出；而面内激励组合下，以2π为变化周期，当相位差为π + 2kπ (k = 0, 1, 2, …)时其对稳态幅值的影响最显著．其原因是：面外激励关于拉索所在的竖直面对称，故其本质上以π为周期；而面内激励无此对称性，仍以2π为周期．因此，有无面外激励参与决定了激励间相位差对斜拉索响应的影响规律．     

拉索预应力巨型网格结构参激振动及动力稳定性研究

针对拉索预应力巨型网格结构的参激振动及动力稳定性问题进行了研究。首先建立索-拱简化模型，分析了桁架拱拉索参激振动的诱发机制与特征，并利用ANSYS软件进一步探究了参激振动的影响因素，然后对简谐荷载作用下拉索预应力桁架拱及整体结构的动力稳定性进行了分析。研究表明：当结构振动频率为索基频的2倍左右时，拉索会发生参激振动，振动响应特征与激励幅值、阻尼、拉索初张力、支承方式等相关；拉索预应力桁架拱在水平简谐荷载作用下一般会发生动力失稳破坏，在竖向简谐荷载作用下发生动力强度破坏，拉索预应力巨型网格整体结构在简谐荷载作用下通常发生动力失稳破坏。     

砂-膨润土混合屏障材料渗透性影响因素研究

建立了一个新的结构-尾流振子耦合模型. 流场近尾迹动力学特征被模化为非线性阻尼 振子，采用van der Pol方程描述. 以控制体中结构与近尾迹流体间受力互为反作 用关系来实现流固耦合. 采用该模型进行了二维结构涡激振动计算，得到了合理的 振幅随来流流速的变化规律和共振幅值，并正确地预计了共振振幅值$A_{\max}^\ast$ 随着质量阻尼参数$\left( {m^\ast + C_A } \right)\zeta $的变化规律，给出了预测$A_{\max }^\ast $值的拟合公式. 采用该模型计算了三维柔性结构在均匀来流和简谐波形来流作用下的VIV 响应. 结构在均匀来流作用下振动呈现由驻波向行波的变化过程, 并最后稳定为行波振动形态. 在简谐波形来流作用下，结构呈现混合振动形态，幅值随时间呈周期变化.     

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.     

圆柱涡激振动的结构-尾流振子耦合模型研究

建立了一个新的结构-尾流振子耦合模型.流场近尾迹动力学特征被模化为非线性阻尼振子,采用vander Pol方程描述.以控制体中结构与近尾迹流体间受力互为反作用关系来实现流固耦合.采用该模型进行了二维结构涡激振动计算,得到了合理的振幅随来流流速的变化规律和共振幅值,并正确地预计了共振振幅值A_(max)~*随着质量阻尼参数(m~*+C_A)ζ的变化规律,给出了预测A_(max)~*值的拟合公式.采用该模型计算了三维柔性结构在均匀来流和简谐波形来流作用下的VIV响应.结构在均匀来流作用下振动呈现由驻波向行波的变化过程,并最后稳定为行波振动形态.在简谐波形来流作用下,结构呈现混合振动形态,幅值随时间呈周期变化.     

An experimental and analytical study of autoparametric resonance in a 3DOF model of cable-stayed-beam

Autoparametric interaction and the associated phenomenon of amplitude saturation are experimentally observed in a physical model of cable-and-beam structure. In this system, the horizontal beam is fixed at one end and supported at the other end by an inclined taut cable. The longitudinal axes of beam and cable are in a vertical plane. Three natural frequencies of the system are approximately of the ratio 1:1:2. This is a combination of two conditions that are very likely to occur in relatively long-span, multi-stay-cable bridges, namely, 1:1 tuning and 1:2 superharmonic tuning. While the beam is vertically excited with sufficiently large force near a primary resonance, the cable vibrates horizontally at half of excitation frequency. The beam also vibrates horizontally at half-frequency, as well as vertically. As the vertical excitation on the bean is further increased in amplitude, the vertical vibration amplitude gets saturated instead of increasing proportionately. A 3DOF analytical model of the structure is also derived, where the finite motion of the cable introduces geometric nonlinearities in quadratic and cubic forms. The system parameters having been carefully measured from the experimental model, steady-state solutions of the coupled nonlinear equations of motion are obtained, by the perturbation method of multiple time scales. Agreement between experimental observation and analytical prediction is very good, both qualitatively and quantitatively. Very good agreement is found also in the case of horizontal excitation of the beam, where effects of linear and nonlinear interaction are apparent.     

In-plane non-linear dynamics of the stay cables

Stay cables used in cable-stayed bridge and cable-stayed arch bridge are prone to vibration due to their inherent susceptibility to external deflection. The present work is devoted to the mitigation of a stay cable from the point of view of its nonlinear dynamics. The Galerkin integral, multiple scales perturbation method, and numerical techniques are applied to analyze the primary and subharmonic resonances of the stay cable. The nonlinear dynamic response of the stay cable subjected to parametrical and forced excitations is investigated numerically. The effects of some key parameters of the stay cable, such as initial tension force, damping and inclination angle, and the excitation frequency and amplitude are discussed. The carbon fiber reinforced polymers (CFRP) cable is also studied to understand the effect of the material properties of cable. The results show that these parameters have a considerable effect on the dynamic behavior of the cable. In particular, unreasonable tension force and inclination angle of stay cable may cause excessive vibration. It is suggested that CFRP cable replaces steel cable, which can mitigate the vibration of a stay cable.     

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。     

FREE VIBRATION OF TAUT CABLE WITH DAMPER AND PARALLEL SPRING

分析了拉索-并联弹簧-阻尼器系统的自由振动特性，由系统的运动方程及边界条件 得到其复特征值方程。进一步研究了系统的极限解，由此讨论了拉索-并联弹簧-阻尼器系统的模态变化分区现象。以拉索-并联弹簧-阻尼器系统的二阶模态解为例，给出了模态频率和阻尼比的变化分布区间及其对应振型的变化情况。讨论了系统分区中存在的模态交叉现象；同时也讨论了斜拉索垂度对于一阶振动模态变化规律的影响。研究表明拉索-并联弹簧-阻尼器系统的振动模态演化因并联弹簧-阻尼器的位置不同而存在的明确的分区现象；安装并联弹簧和阻尼器后拉索的模态阻尼比和模态频率均可明显提高。     

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.     

A unified approach to aerodynamic damping and drag/lift instabilities,and its application to dry inclined cable galloping

Inclined cables of cable-stayed bridges often experience large amplitude vibrations. One of the potential excitation mechanisms is dry inclined cable galloping, which has been observed in wind tunnel tests but which has not previously been fully explained theoretically. In this paper, a general expression is derived for the quasi-steady aerodynamic damping (positive or negative) of a cylinder of arbitrary cross-section yawed/inclined to the flow, for small amplitude vibrations in any plane. The expression covers the special cases of conventional quasi-steady aerodynamic damping, Den Hartog galloping and the drag crisis, as well as dry inclined cable galloping. A nondimensional aerodynamic damping parameter governing this behaviour is proposed, which is a function of only the Reynolds number, the angle between the wind velocity and the cable axis, and the orientation of the vibration plane. Measured static force coefficients from wind tunnel tests have been used with the theoretical expression to predict values of this parameter. Two main areas of instability (i.e. negative aerodynamic damping) have been identified, both in the critical Reynolds number region, one of which was previously observed in separate wind tunnel tests on a dynamic cable model. The minimum values of structural damping required to prevent dry inclined cable galloping are defined, and other factors in the behaviour in practice are discussed.     

考虑横向惯性效应的非饱和土中单桩的竖向动力响应

基于非饱和土的动力控制方程,考虑横向惯性效应,建立了三相非饱和介质中嵌岩桩的竖向动力响应连续介质模型,对桩侧非饱和土的动力控制方程进行Laplace变换,在频域内,通过引入势函数、算子分解等手段对控制方程进行解析,得到了桩侧土体剪应力及竖向振动位移的表达式.结合桩基的竖向振动方程及桩–土接触面的连续性条件,使桩土耦合振动系统得以解答,最终在频域内得到了桩顶复刚度、导纳、桩–土系统振动位移及应力的解析解,借助Laplace逆变换得到了半正弦激励载荷下桩顶的速度时程曲线.最后,通过算例分析验证了计算结果的准确性,分析了横向惯性、泊松比、饱和度、长径比、桩土模量比等因素对桩基动力响应的影响.结果表明:(1)单桩动刚度、阻尼、导纳等变量随频率变化发生周期性振荡,在桩基各阶固有频率处发生共振;(2)泊松比、饱和度、长径比、桩土模量比等因素对桩基的动力响应有较大影响,且频率越大,影响越明显;(3)泊松比越大,单桩动刚度、阻尼、导纳的波动幅值及对应的频率越小,桩顶时程曲线中的桩底反射信号越弱;(4)饱和度越大,对应各动力响应的波动幅值越大,且桩底反射信号的波峰越大.     

S型测力传感器的动态特性与标定

本文对 S 型测力传感器的动态特性进行了研究。采用模态分析测量技术,测定了传感器的固有频率、模态质量、模态刚度、模态阻尼和阻尼比,并以动画形式显示了其主振型.作出激振力与传感器应变片输出信号的传递函数幅频和相频特性曲线,可简便地确定传感器工作频率范围及相应的误差。     

Nonlinear vibration of fluid-conveying single-walled carbon nanotubes under harmonic excitation

In this paper, the nonlinear vibration of a single-walled carbon nanotube conveying fluid is investigated utilizing a multidimensional Lindstedt–Poincaré method. Considering the geometric large deformation of the single-walled carbon nanotube and external harmonic excitation force, based on nonlocal elastic theory and Euler–Bernoulli beam theory, the nonlinear vibration equation of a fluid-conveying single-walled carbon nanotube is established. Analyzing the equation through the multidimensional Lindstedt–Poincaré method, and from the solvability condition of the nonlinear vibration equation, the cubic algebraic equation which indicates the amplitude–frequency relation is obtained. Based on the root discriminant of the cubic equation, the first order primary response of the pinned–pinned carbon nanotube is discussed. The relations among internal resonance, the amplitude and frequency of the external excitation force are analyzed in detail. When the external excite force frequency is around the first mode natural frequency, the first mode primary resonance occurs. If simultaneously the first two modes natural frequency ratio is around 3, internal resonance occurs and the internal resonance region depends on the amplitude of external excitation force.