超长柔吊装臂架回转作业刚柔耦合动力学模型与分析

针对超长柔臂架系统在回转吊装运动中的非线性动力学行为,开展了模型构建与振动特性分析。考虑大型起重机臂架的刚柔耦合运动特征与吊装大挠度效应,利用混合坐标系描述了吊臂刚柔耦合运动,在臂头随动坐标系上描述吊重与钢丝绳的偏摆运动;通过初应力法构建了结构的几何非线性刚度矩阵;采用拉格朗日方程,推导并给出了综合考虑超长柔臂架刚柔耦合效应、几何非线性效应、惯性力效应的动力学分析模型。通过对某轮式起重机的动力仿真分析,结果表明:超长柔臂架在吊臂几何非线性效应影响下,吊重偏摆幅度增大,周期延长;吊载愈重,几何非线性效应对吊臂振动及吊重摆动的影响愈明显;轻载吊装吊臂振动主要由回转惯性力引起,但重载时吊臂振动规律取决于吊重偏摆振动。分析结果为臂架结构设计及控制系统设计提供了依据。     

绳索系统的建模、动力学和控制

绳索系统具有无限自由度,当计入非线性因素的作用时,其面内和面外的振动相互耦合,呈现非常丰富的非线性动力学行为.另外,绳索系统经常工作在风、流体、微重力、电磁力等作用下,进一步加剧了其动力学的复杂性.绳索系统的动力学现象引起了工程界和力学界的关注.本文对绳索在重要工程系统中的应用及相应的动力学现象进行概述,给出了柔索的动力学建模过程,对绳索系统的动力学和控制研究进行了总结,并指出了值得进一步关注的若干问题.      

绳索的大变形问题

根据绝对柔韧杆在大变形时应变与位移的准确关系以及平衡方程;推导出绳索在自重作用下的精确关系以及平衡方程,推导出绳索在自重作用下的精确解析解．并举例对电缆进行了分析和讨论．     

滑轮绳索系统中动态节点绳索单元

解除了传统有限元方法中单元节点与物质点固结的假设, 建立了空间点的速度和加速度与相应物质点的速度和加速度之间的数学关系, 强调了虚功率原理中出现的速度和加速度皆为物质速度和物质加速度. 在此基础上构造了单元节点既不与空间坐标固定也不与物质坐标固定的动态节点绳索单元. 根据滑轮绳索系统的特点, 选取绳索出入绳点的弧长坐标、出入绳角、面外摆角以及拉伸应变等空间参数描述了滑轮绳索系统的运动. 将绳索与滑轮以及绳索与卷筒之间的相互作用合理简化为物质速度间的约束条件, 避免了传统方法中接触力计算不收敛、效率低等缺点. 所提方法可精细求解绳索与滑轮间接触边界点位置和卷筒入绳点在卷筒上的运动、滑轮的中心和其连体基的运动、绳索出入滑轮和卷筒时空间方位的变化以及绳索上任意点的拉力变化等细节. 可为含绳索机械系统的力学分析提供新的理论基础. 所用的解除单元节点与物质点绑定的理论具有一定的普适性, 可为有限元方法的理论和应用提供参考.      

旋涡与行进表面水波相互作用的实验研究

采用振动板式造波器在二维水槽中生成近似单色的行进表面水波，采用夹板式涡发生器生成稳定上浮的涡对，在Ｆｒｏｕｄｅ数约为０．５的条件下，得到了水下涡对与不同波长和振幅的行进表面水波相互作用时的干扰图象，以实验方法验证了理论分析和数值计算的结果，并为进一步研究旋涡与行进表面水波的相互作用提供了一种实验研究方法     

捷联惯导基于地球系的动基座间接精对准算法

为了将惯性凝固思想延伸到行进间精对准中并提升计算效率,提出了基于地球系的间接精对准算法。描述了地球系下的捷联惯导/里程计系统模型和相应的Ψ角误差模型。考虑安装偏差角、杆臂等因素,建立了相应的卡尔曼滤波方程。六组行车轨迹的行进间对准结果表明,相对于地理系精对准算法,地球系间接算法整体对准性能更加优越,系统的稳定性和快速性得到提高,在对准第600 s方位失准角可以稳定在1 mil(1σ)的误差限内。另外,地球系滤波算法具有更好的初始化参数适应性,有利于工程实现。     

具有间歇性缺陷的混合流体行进波对流斑图

本文通过流体力学基本方程组的数值模拟,探讨了具有中等Soret效应的混合流体行进波斑图的动力学特性.当分离比Ψ=-0.3时,首次发现一种没有源缺陷的左右相对传播的CPW(Counter propagating waves)状态向行进波状态的过渡形式,并且在r=1.50-1.60的范围内,行进波对流斑图中存在着间歇性缺陷结构.这种缺陷出现的周期随瑞利数r增大而增加.在缺陷出现的周期内,对流振幅也以行进波的周期在周期的变化,对流振幅的振动次数或行进波的周围数也随相对瑞利数r增大而增加.当r增加到1.65时,行进波对流斑图中的缺陷结构消失.由于缺陷引起的对流振幅的周期性变化也随之消失,而以行进波的周期在整个时间段上周期的振动.     

里程计辅助陆用惯导行进间对准方法

行进间对准技术能够使惯导在运动状态下完成系统初始化,它对于提高载体机动能力具有重要作用。与静基座对准不同,行进间对准通常需要利用外部设备(在陆用导航领域,通常使用GPS或里程计)提供载体运动信息对惯性导航系统输出进行补偿和修正。由于里程计辅助的行进间对准具有全自主的特点,因而被广泛采用。本文通过对里程计误差进行合理建模,并采用位移增量匹配方法实现了里程计和惯导系统的组合。同时,针对复杂路面环境下由于车体侧滑、空转等造成里程计测量失准等故障现象进行有效诊断,以此提高了组合导航系统的可靠性。通过行进间对准试验,结果表明由里程计辅助的惯导系统经过10 min初始对准,航向误差小于0.05°,精度和静基座相当。     

具有大范围回转和伸缩运动的柔性机械臂动力学建模与分析

大范围转动和伸缩运动是某些机械臂系统的典型运动特征,如快堆中燃料组件转运机构.为了实现精准定位操作,设计过程中需要考虑机械臂的弹性振动问题．本文从刚体运动和弹性变形耦合的角度出发,运用广义Hamilton原理建立了一种变长度回转梁的时变动力学方程．通过变量替换,利用假设模态法得到二阶变系数微分方程,并采用Newmark-β法进行求解．根据计算结果,讨论了不同回转角速度和轴向伸缩情形对机械臂末端弹性振动的影响,并说明了在此类柔性机械臂振动分析中考虑刚弹耦合的必要性．     

具有大负分离比的混合流体局部行进波对流

从流体层底部加热引起的对流运动是研究非平衡对流的时空结构或斑图(Pattern)及非线性动力学特性的典型模型之一.本文通过流体力学基本方程组的数值模拟,探讨了具有强Soret效应的混合流体局部行进波的形成过程,发现当分离比ψ=-0.6时,在局部行进波的存在范围内,向局部行进波过渡的不同过程依赖于相对瑞利数r.进一步,讨论了具有强Soret效应的混合流体局部行进波流速场,温度场, 浓度场的结构和特性,分析了局部行进波的存在区间对分离比ψ的依赖性.发现随着Soret效应的增强或负分离比ψ的绝对值的增加,局部行进波稳定存在的区间Δr也在增加.     

Stretch and Rotation of a Suspended Cable Subject to Transverse Fluid Excitation

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Static and dynamic response of elastic suspended cables with damage

In cable-stayed structures cables are subjected to potential damage, mainly due to fatigue and galvanic corrosion. The paper presents an analysis of damage effects on the statics and dynamics of suspended cables. An elastic continuous monodimensional model for damaged cables, including geometric nonlinearities, is formulated for the purpose. The damage is described as a diffused reduction of the cable axial stiffness, and defined through its intensity, extent and position. Exact solutions of the equations governing the cable static equilibrium under self-weight are achieved, and the significance of the tension loss and sag augmentation resulting from damage are investigated under variation of practically significant parameters. The system spectral properties characterizing the free undamped dynamics are obtained in a closed-form fashion for shallow cables within the low frequency range. The sensitivity of the frequencies to the intensity and extent of damage is discussed, outlining two damage effects, which alternatively stiffen or soften the cable modes, whose respective static and geometric origin is recognized. Finally, the symmetry-breaking induced by damage on the static profile is verified to destroy the crossing phenomenon (crossover) characterizing the frequency loci of undamaged cables, which degenerates into a narrow frequency veering phenomenon.     

NONLINEAR VIBRATION OF THE COUPLED STRUCTURE OF SUSPENDED-CABLE-STAYED BEAM-1:2 INTERNAL RESONANCE

Through the Galerkin method the nonlinear ordinary differential equations （ODEs） in time are obtained from the nonlinear partial differential equations （PDEs） to describe the mo- tion of the coupled structure of a suspended-cable-stayed beam. In the PDEs, the curvature of main cables and the deformation of cable stays are taken into account. The dynamics of the struc- ture is investigated based on the ODEs when the structure is subjected to a harmonic excitation in the presence of both high-frequency principle resonance and 1：2 internal resonance. It is found that there are typical jumps and saturation phenomena of the vibration amplitude in the struc- ture. And the structure may present quasi-periodic vibration or chaos, if the stiffness of the cable stays membrane and frequency of external excitation are disturbed.     

Bifurcations and chaotic dynamics in suspended cables under simultaneous parametric and external excitations

The bifurcations and chaotic dynamics of parametrically and externally excited suspended cables are investigated in this paper. The equations of motion governing such systems contain quadratic and cubic nonlinearities, which may result in two-to-one and one-to-one internal resonances. The Galerkin procedure is introduced to simplify the governing equations of motion to ordinary differential equations with two-degree-of-freedom. The case of one-to-one internal resonance between the modes of suspended cables, primary resonant excitation, and principal parametric excitation of suspended cables is considered. Using the method of multiple scales, a parametrically and externally excited system is transformed to the averaged equations. A pseudo arclength scheme is used to trace the branches of the equilibrium solutions and an investigation of the eigenvalues of the Jacobian matrix is used to assess their stability. The equilibrium solutions experience pitchfork, saddle-node, and Hopf bifurcations. A detailed bifurcation analysis of the dynamic (periodic and chaotic) solutions of the averaged equations is presented. Five branches of dynamic solutions are found. Three of these branches that emerge from two Hopf bifurcations and the other two are isolated. The two Hopf bifurcation points, one is supercritical Hopf bifurcation point and another is primary Hopf bifurcation point. The limit cycles undergo symmetry-breaking, cyclic-fold, and period-doubling bifurcations, whereas the chaotic attractors undergo attractor-merging, boundary crises. Simultaneous occurrence of the limit cycle and chaotic attractors, homoclinic orbits, homoclinic explosions and hyperchaos are also observed.     

考虑弯曲刚度斜拉索面内面外内共振分析

本文研究桥梁工程中含弯曲刚度斜拉索的面内面外内共振问题．描述了工程中斜拉索变形的三种状态,考虑弯曲刚度、大变形及垂度等因素,忽略斜拉索纵向惯性力的影响,运用Hamilton变分原理建立了含弯曲刚度的斜拉索面内面外耦合偏微分控制方程,采用Galerkin方法对偏微分方程离散,并运用多尺度摄动方法进行了求解,获得了斜拉索可能存在的内共振模式,以工程中一根斜拉索为例,运用有限元法对其进行动力特性分析,列出了斜拉索前10阶面内面外振动频率,找出面内面外可能产生内共振的模态,分别研究了主共振条件下斜拉索面内和面外1:1、2:1内共振情形,获得了有意义的结论．     

TWO-DIMENSIONAL VORTEX-INDUCED VIBRATION OF CABLE SUSPENSIONS

Resonant responses of suspended elastic cables driven by a steady current are investigated. Phenomenological fluid force models for alternate vortex-shedding are coupled with the nonlinear partial differential equations of cable motion. Decoupled cross-flow and in-line vortex-induced vibrations (VIV) are examined first using linearized and nonlinear cable models. The linearized cable model predicts well the basic characteristics of VIV and the nonlinear cable model captures the hysteresis often observed in experiments. Next, coupled cross-flow and in-line vibrations are evaluated by considering two principal coupling mechanisms: (i) cable structural nonlinearities, and (ii) coupled fluid lift and drag. Attention is focused on a “worst-case” resonant response where the natural frequencies for cable modes in the cross-flow and in-line directions are in the same 1:2 ratio as the excitation frequencies associated with lift and drag. The inclusion of cable structural nonlinearities alone leads to coupled responses that differ qualitatively (i.e., in number and stability of periodic motions) when compared to those of the decoupled model. The inclusion of coupled fluid lift and drag produces non-planar “figure eight” motions of the cable cross-section that exhibit similar characteristics to those previously measured on spring supported cylinders.     

Dynamic instability of inclined cables under combined wind flow and support motion

In this paper an inclined nearly taut stay, belonging to a cable-stayed bridge, is considered. It is subject to a prescribed motion at one end, caused by traveling vehicles, and embedded in a wind flow blowing simultaneously with rain. The cable is modeled as a non-planar, nonlinear, one-dimensional continuum, possessing torsional and flexural stiffness. The lower end of the cable is assumed to undergo a vertical sinusoidal motion of given amplitude and frequency. The wind flow is assumed uniform in space and constant in time, acting on the cable along which flows a rain rivulet. The imposed motion is responsible for both external and parametric excitations, while the wind flow produces aeroelastic instability. The relevant equations of motion are discretized via the Galerkin method, by taking one in-plane and one out-of-plane symmetric modes as trial functions. The two resulting second-order, non-homogeneous, time-periodic, ordinary differential equations are coupled and contain quadratic and cubic nonlinearities, both in the displacements and velocities. They are tackled by the Multiple Scale perturbation method, which leads to first-order amplitude-phase modulation equations, governing the slow dynamics of the cable. The wind speed, the amplitude of the support motion and the internal and external frequency detunings are set as control parameters. Numerical path-following techniques provide bifurcation diagrams as functions of the control parameters, able to highlight the interactions between in-plane and out-of-plane motions, as well as the effects of the simultaneous presence of the three sources of excitation.     

Nonlinear transient response of stay cable with viscoelasticity damper in cable-stayed bridge

Taking the bending stiffness, static sag, and geometric non-linearity into consideration, the space nonlinear vibration partial differential equations were derived. The partical differential equations were discretized in space by finite center difference approximation, then the nonlinear ordinal differential equations were obtained. A hybrid method involving the combination of the Newmark method and the pseudo-force strategy was proposed to analyze the nonlinear transient response of the inclined cable-dampers system subjected to arbitrary dynamic loading. As an example, two typical stay cables were calculated by the present method. The results reveal both the validity and the deficiency of the viscoelasticity damper for vibration control of stay cables. The efficiency and accuracy of the proposed method is also verified by comparing the results with those obtained by using Runge-Kutta direct integration technique. A new time history analysis method is provided for the research on the stay cable vibration control.     

斜拉桥拉索在轴向窄带随机激励下的振动响应

导出了拉索在考虑垂度以及索张力沿索长变化时的参激随机微分方程,进一步给出了预测拉索在窄带随机激励下响应的近似理论解------用统计矩截断法求解矩方程,获得高斯闭合解和一阶非高斯闭合解. 以南京长江二桥约330米长的A20拉索为研究对象,对以上高斯闭合解和一阶非高斯闭合解进一步进行数值求解以获得拉索的响应,并采用Monte-Carlo数值方法对求解进行验证. 分析了拉索振动的一般特征,特别分析了激励中心频率和拉索频率比为1和2时的响应随激励带宽的变化特征,得到了一些新的结论.      

考虑非稳态风荷载斜拉索风雨激振响应分析

为研究自然风荷载对斜拉桥拉索风雨激振的影响,将数值模拟的非稳态风荷载作用到拉索振动微分方程中,对拉索振动响应进行了详细分析。首先,针对水线初始位置,使用最小二乘法拟合得到水线初始位置方程;接着,采用四阶Runge-Kutta法求解拉索振动响应。通过比较在非稳态风和稳态平均风作用下的拉索响应,发现在非稳态风荷载下拉索最大振幅的变化趋势并没有发生较大改变,皆是随着风速的增大先增大后减小;但拉索的整个振动过程发生了变化,伴随着节拍改变,其最大振幅也出现在不同振动周期内。此外,从风速-振幅曲线知,对频率为1 Hz,2 Hz和3 Hz的拉索,在一定风速范围内,考虑非稳态风荷载的拉索振幅反而更大,而且此时的风速范围也更大。