索梁结构中抗弯刚度斜拉索的非线性响应

研究索梁结构中考虑抗弯刚度斜拉索的非线性响应.从斜拉桥中简化出索梁组合结构力学模型,考虑抗弯刚度、几何非线性及垂度等因素,忽略索梁纵向振动,基于Hamilton变分原理,获得了索梁结构耦合非线性振动偏微分方程组.首先运用Galerkin方法离散该方程组,然后利用多尺度法对该方程组进行摄动分析.以某索梁结构为例,分析了索主要参数对抗弯刚度斜拉索面内基频的影响,探讨了抗弯刚度对斜拉索幅频响应、激频响应的影响,数值模拟获得了索梁结构的时程曲线.结果表明,考虑抗弯刚度后,索长对斜拉索面内基频的影响较大,对于短索,应考虑抗弯刚度;含抗弯刚度斜拉索的幅频响应曲线整体向右平移,激频响应曲线向左移,移动的幅度取决于抗弯刚度的大小;梁振动将对索振动产生显著影响,索振动对梁的振动影响很小.     

杆网系统基于高斯原理的动力学建模

讨论由任意数量弹性细杆组成任意拓扑结构的杆网系统.叙述其基于高斯最小拘束原理的动力学建模方法.其工程背景为航天技术中的可展网架式结构.采用Kirchhoff模型描述弹性杆的运动,其大变形的幅度可不加限制.导出杆网系统拘束函数的普遍形式及联结铰对杆件的几何约束条件.所述动力学模型可直接应用变分方法确定杆网系统的运动,无需建立和求解动力学微分方程.利用拘束函数的最小值条件从杆件的各种可能运动中确定其真实运动.联结铰的约束条件可在供选择的可能运动中预先给予满足.对于杆件充分柔软的特殊情形,忽略其抗弯和抗扭刚度,但考虑其拉伸变形,则杆网系统转化为由柔索组成的索网系统.以5杆系统为例说明此建模过程.     

弹性细杆弯扭度有突变时的Lagrange方程

根据弹性细杆静力学的Kirchhoff动力学比拟方法,将弹性细杆截面的弯扭度和形心应变矢有突变的弹性变形比拟为动力学中的打击运动现象.分别从精确Cosserat弹性细杆和Kirchhoff弹性细杆静力学的Lagrange方程出发,导出了弯扭度和形心应变矢有突变时的Lagrange方程,其形式与打击运动的Lagrange方程形式相同.分析了弯扭度和形心应变矢的突变对挠曲线光滑性的影响.为弹性细杆弯扭度有突变时的平衡分析提供分析力学方法.     

漂浮式斜拉桥全局模态对CFRP索的敏感性研究

斜拉桥复杂动力学问题中的一个关键问题是局部模态频率与全局模态频率成倍数匹配关系时可能导致的斜拉索大幅振动.本文针对这个问题,基于传递矩阵法,研究CFRP索对斜拉桥全局模态频率的敏感性.将斜拉桥的桥面梁和桥塔分别视为多离散弹性支承欧拉伯努利梁,建立其动力学控制微分方程,基于传递矩阵法对其特征频率进行求解.以长沙某独塔斜拉桥作为算例,对结构主要构件:斜拉索、塔和桥面梁的刚度变化对全局模态频率变化的敏感性问题进行了分析.结果表明,桥面梁和桥塔全局模态频率对斜拉索刚度变化非常敏感,并且用CFRP索替换钢质拉索可能避开拉索局部模态与斜拉桥全局模态的倍频关系,从而控制斜拉索的大幅振动.     

受力螺旋作用的非圆截面弹性直杆的Lyapunov稳定性

基于Kirchhoff动力学比拟思想,研究非圆截面压扭弹性细直杆的Lyapunov稳定问题．用Cardano角表示截面的姿态,根据Kirchhoff方程建立杆的平衡微分方程,得到了两端受力螺旋作用时的直线平衡特解,导出了具有周期系数的线性化扰动方程,其周期与扭矩和杆长成正比,与抗扭刚度成反比,圆截面情形为其特例．用Floquet理论讨论了其Lyapunov稳定性,算例表明对于给定的弹性杆,扭矩和压力对稳定是有利的,而拉力是不稳定的主要因素．     

弹性细杆的混沌形态

讨论端部受扭矩作用的非圆截面弹性杆平衡形态的混沌现象.混沌的产生来源于抗弯刚度的微幅周期变化.基于Kirchhoff动力学比拟理论列写弹性杆的平衡方程.应用Melnikov方法的解析预测以及Poincar啨截面和相轨?氖导扑阒っ鞯愿司哂蠸male马蹄意义下的混沌形态.给出混沌性态与规则性态所对应弹性杆几何形状的对照.     

松弛状态非圆截面弹性螺旋细杆的稳定性

研究松弛状态下的非圆截面弹性螺旋细杆,即带有原始曲率和挠率的非圆截面弹性杆的平衡稳定性问题．基于Kirchhoff动力学比拟,建立用欧拉角表达的弹性杆动力学方程．忽略线加速度引起的微小惯性力,仅考虑截面转动的动力学效应,使欧拉方程封闭．证明松弛状态下的非圆截面螺旋杆无论在空间域或时域均满足一次近似意义下的Lyapunov稳定性条件．从而为螺旋形态弹性细杆存在于自然界中的广泛性和稳定性作出理论解释．提示负泊松比材料的螺旋杆可能不稳定．     

斜拉索主参数共振的稳定性分析

研究轴向激励下斜拉索的主参数共振的稳定性问题．考虑拉索垂度和几何非线性的影响,导出了拉索在轴向激励下的非线性参数振动方程．利用多尺度方法研究了斜拉索的主参数共振问题,并对其稳态解的稳定性作了较详细的分析．对斜拉索的主参数共振进行了数值模拟,得到了不同阻尼、初始条件及激励幅值作用下拉索的时程曲线．结果表明：斜拉索的固有频率与外激励参数对斜拉索稳态解的个数及其稳定性都存在直接影响,从而对斜拉索的参数设计起到了指导作用．     

斜拉桥张拉索张力的测定

基于斜拉桥拉索的受力特点,提出一种索张力测定的新方法.文中研究了索张力传感器的测试机理,导出了传感器测力信号与索张力的关系.研究结果表明:该测试方法能有效地消除支座条件、拉索自重及索抗弯刚度等因素对测力信号的影响,可实现斜拉桥张拉索受力的精确、快捷测量.     

斜拉桥中拉索对桥面动力特性的影响

将斜拉桥的拉索和桥面抽象为带弹性支承的压弯弹性梁模型,并根据轴向受力梁的弯曲振动方程和哈密尔顿原理,建立了考虑拉索索力影响的单梁多索索梁结构-梁的动力学控制方程,应用传递矩阵法进行求解,并编制了求解程序.通过算例对影响桥面动力学特性的索的刚度、张拉力和桥面裂纹等因素进行了数值分析.分析结果表明,在斜拉桥的施工阶段,随着梁的长度的改变,梁的刚度讯速下降,由于索对梁的支承作用使结构的刚度有一定的提高,而索的拉力对桥面作用的压力越来越大,轴向压力使结构的刚度降低越来越明显,另一方面轴向压力对桥面裂纹引起的刚度降低有一定的抑制作用.由此,在桥梁的建设中应重视索力对桥面动力特性的影响.     

基于Cosserat 弹性杆理论的柔性线缆物理建模方法

针对虚拟环境中线缆敷设过程仿真的线缆建模问题,提出一种基于Cosserat 弹性 杆理论的柔性线缆物理建模方法。该方法在线缆离散模型的基础上根据Cosserat 弹性杆理论导 出线缆的总体势能,并通过优化算法得到线缆总体势能最小时的线缆形态,即线缆的平衡状态。 模型考虑到线缆的柔性和连续性,能够模拟线缆的弯曲和扭转变形;通过对线缆进行离散表达, 实现了对线缆总体势能的数值求解;引入罚函数将求解线缆总体势能最小值问题转化为非线性 无约束优化问题;非线性无约束优化问题的求解采用信赖域方法,提高了求解的稳定性。设计 并开发了虚拟环境中的线缆敷设过程仿真原型系统,并进行实例验证,证明该方法的可行性。     

A novel scheme for large deflection analysis of suspended cables made of linear or nonlinear elastic materials

This paper presents a new approach to investigate the static response of horizontal and inclined suspended cables with deformable cross-section, made of general linear or nonlinear elastic materials, and subjected to vertical concentrated and distributed loads. The proposed technique also includes large sag and extensibility effects, and is based on an original finite difference scheme combined to a nonlinear least squares numerical solution. The mathematical formulation is developed for various loading cases, and an innovative computational strategy is used to transform the resulting nonlinear system of equations into a scaled nonlinear least squares problem. The numerical scheme is programmed and its application illustrated through examples highlighting the effects of coupling between the tension in a cable and the deformation of its cross-section as well as the use of cables made of neo-Hookean materials. The results obtained are in excellent agreement with analytical solutions when available. The proposed technique can be easily programmed and constitutes a valuable tool for large deflection analysis of suspended cables made of nonlinear elastic materials.     

Initial shape of cable-stayed bridges

A finite element computation procedure for determining the initial shape of cable-stayed bridges under the action of the dead load of girders and pretension in inclined cables is presented. The system equation of cable-stayed bridges including the nonlinearities due to large displacement, beam-column, and cable sag effects is first set up and then solved using the Newton-Raphson method in an increment-iterationwise approach. Based on a reference configuration and an assumed cable pretension force, the equilibrium configuration under dead load is found. Further, by adjusting cable forces, a ‘shape iteration’ is carried out and a new equilibrium configuration, i.e., a more reasonable initial shape, can be determined. The shape iteration is repeated until the desired tolerance is achieved. Numerical results show that a more accurate initial shape having reasonable prestress distribution and less deflection of girders can easily be determined by the proposed procedure.     

On the inverse kinematics,statics, and fault tolerance of cable-suspended robots

This paper examines some issues concerning the inverse kinematics and statics of cable-suspended robots and studies some of the inherent workspace limitations that result from the fact that the robot is cable actuated. The paper presents necessary and sufficient conditions for a cable-suspended robot to stay in a given configuration (i.e., to achieve static equilibrium). Another important issue is the extent to which the cables constrain the robot. For example, fully constraining the robot is critical for space applications in which the robot must work in a zero-gravity environment. Conditions for completely constraining the robot are derived. The problems of achieving static equilibrium and fully constraining the robot are formulated in terms of the left null space of a manipulator inverse Jacobian. This null space formulation is also used to study the fault tolerance of cable-suspended robots that are redundantly actuated. © 1998 John Wiley & Sons, Inc.     

Analysis of target configurations under dead loads for cable-supported bridges

This paper presents a rigorous approach for analyzing the target configurations of cable-supported structures under dead loads by the Newton–Raphson method. A linearized equilibrium equation of a cable element, which includes the nodal coordinates and the unstrained element length as unknowns, is formulated using the analytical solution of an elastic catenary cable. An incremental equilibrium equation for a single cable is formed with the proposed equilibrium matrices of cable elements. The geometry of the target configuration of a cable-supported structure under dead loads is utilized to solve the incremental equilibrium equation. Detailed procedures to analyze the target configurations of suspension bridges and cable-stayed bridges are presented. The efficiency and the accuracy of the proposed method are demonstrated through numerical examples.     

多档货运索道动力计算方法及结构冲击影响研究

根据多档索道工作索(承载索和牵引索)及运行小车的相互作用关系,基于有限质点法理论建立质点运动方程,构建了适用于多档货运索道整体结构的动力计算方法.在计算方法中,采用索滑移单元的方式模拟工作索与支架、载荷的滑移接触状态,并提出牵引索循环行进计算方法.应用构建的整体计算方法分析了载荷质量、牵引机牵引速度及承载索长度等主要影响因素作用下运行小车通过货运索道支架时的冲击动力响应,给出了承载索、牵引索及支架的张力变化情况,对实际工程中货运索道钢丝绳、支架等结构的动态冲击性能提出技术要求,可为多档货运索道的设计提供更加科学合理的参考依据.     

Nonlinear structural models in cableway transport systems

In this paper an analysis of the nonlinear static behaviour of cable systems is developed by assuming a full nonlinear structural model of the cables based on elastic catenary results. The work is aimed at the possible application of this kind of structure to practical engineering systems such as among others ski lifts, electrical transmission lines, and cable systems in erection procedures of long-span bridges. The structural model is then implemented in a suitable computer code program able to analyse strong nonlinearities arising from low stress levels in the cables, where the uniqueness of the solution is not assured. Therefore, an appropriate simulation technique is required to capture the static equilibrium configurations of the cable systems subjected to a given external action. After a preliminary discussion of the relevant equations governing the behaviour of the structural model, a finite element analysis is developed to account for the main inherent features related to convergence and stability of the numerical algorithm used. Then, some illustrative numerical examples are developed by suitably calibrating the input data in such a way that strong nonlinearities stand out which enable the checking of the validity of the present analysis.