【作者】 何亮；

【导师】 肖南；

【作者基本信息】 浙江大学 ， 结构工程， 2006， 硕士

【摘要】 由于拉索受力过程中大位移小应变的特点,表现出较强的非线性性能,准确分析拉索的静、动力特性是拉索体系设计分析的重要工作之一。索的非线性动力学行为的研究是一个很复杂的课题,本文在继承前人研究成果的基础上,从理论的角度集中于对拉索各自由度之间以及拉索与结构之间的非线性动态耦合特性进行研究。 本文在P.Warnitchai提出的拉索非线性动力模型的基础上,把拉索复杂的动力行为区分为固定边界条件下的模态运动和可动边界条件下的参数运动两种形式,以分别体现拉索自身不同模态、不同自由度之间的“自耦合”现象和拉索与结构之间的“互耦合”现象。运用Newton运动学原理,两种运动的结合可完整表述拉索的动力模态运动。此外,对于拉索体系的动力学分析而言,本文的方法是先对整体结构用有限元方法得出它的低阶固有频率,然后与每根索的固有振动频率进行比较,选出可能产生模态共振或参数共振的索单独进行研究。 基于这种思路,为了全面分析单索的非线性动力学行为,本文首先建立了描述索元三维运动状态的向量表达式,推导了反映拉索运动状态与索内动拉力变化之间关系的变形协调方程,接着用D’Alembert原理建立了弹性拉索考虑几何非线性的三维运动平衡方程。 在此基础之上,本文利用Galerkin方法并根据索的线性振动模态,得到了反映面内一阶模态与面外一阶模态耦合特征的二自由度模态振动平衡方程以及非平面运动边界条件下反映拉索轴向、面内及面外一阶模态耦合特征的空间非线性参数振动平衡方程。利用多尺度摄动法对拉索的内共振、受迫振动、参数振动等运动情况进行求解,研究了拉索的频率匹配关系、稳态周期运动、频率响应方程等动力特征。 拉索运动过程中的索内动拉力变化情况是拉索设计分析的关键环节。由于用解析方法很难得到相关信息,而数值方法可以得到一些更有意义的结论。在理论研究的基础上,本文以具体的斜拉索为例,考虑索内动拉力变化与拉索运动状态变化之间的耦合影响,根据本文建立的变形协调方程,编制了拉索耦合振动系统的计算程序并利用该程序对拉索跨中的位移响应及索内动拉力的时间历程进行了数值分析,得到的结论可以为拉索的设计分析提供一些帮助。此外,用数值方法还对拉索的一阶模态频率、振动响应幅值及系统阻尼影响等特性进行了研究。 论文的最后对上述研究内容及主要成果作了总结,突出了拉索共振情况下索内动拉力变化影响的重要性,并指出了进一步研究工作的方向。更多还原

【Abstract】 Cables are very efficient structural members and hence have been widely used in many long-span structures, including cable-supported roofs, cable-supported bridges, cable-stayed reticulated grid structures and guyed towers. Since cables are very flexible, low damping and light weight, stuctures with cables usually possess complex static and dynamic behaviors. The accurate analysis of both static and dynamic behavior is very important for design of cables in cable-structures. Numerous papers have studied the dynamic behaviors of cable nonlinear vibrations because of their geometric nonlinearity. Based on them, this thesis is devoted to the theoretical and numerical investigations of the nonlinear dynamic coupled effect between the different degrees of freedom in inclined cables and the effect between cables and structures.With the reference of the nonlinear dynamic model firstly present by P. Warnitchai, cable complex motions are separated into modal motions and parametric motions in this thesis. The modal motions are expressed as a combination of the linear undamped modes of a cable with fixed ends which presents the previous coupled effect above, and the parametric motions are the displacements of the cable which moves as an elastic tendon due to the support movements which presents the other. By Newton’s kinematic principle, a combination of the two distinct motions may describe the complete dynamic behaviors of cables. As for the dynamic analysis approach of cable systems in this thesis, the finite element method is used to obtain the low-order natural frequencies of the overall structure and then compared them with the natural frequency of each cable. Thus the cable which can generate internal resonance vibration or parametric resonance vibration will be studied individually.Therefore, vector representations for describing motion states of the three-dimensional infinitesimal cable elements are established firstly in Chapter 2 for obtaining the rounded analysis of nonlinear dynamic behaviors. And then the deformation compatibility equations that represent the relation between motion state and dynamic prestress in cables are deduced. Finally, a three-dimensional nonlinear dynamic equilibrium equation is proposed according to the principle of D’Alembert.The thesis assumes that dynamic motion of the chord-wise cable is in its linear mode. Then the two-DOF dynamic equilibrium equation which reveals coupled effect between the modal motions in-plane and the modal motions out-of-plane based on the definition in Chapter 2, and the three-DOF non-linear dynamic equilibrium equation which reveals coupled effect among axial, in-plane and out-of-plane parametric motions are proposed in Chapter 3 and Chapter 4 respectively according to Galerkin method. The analysis of dynamic phenomena in cable, such as internal resonance, forced vibration, parametric vibration and so on, is carried out by using the multiple scales method which is devoted to the dynamic characteristic investigations of frequency matching relations, periodic steady-state motions, frequcncy response equations, etc.The amplitude of variation for dynamic prestress is generally in a wide domain when cables generateresonant phenomena and it is a critical aspect in design of cable-structures. For numerical method is an efficient approach which could obtain more significative information in cable-structure analysis. Therefore, taking the coupled effect between dynamic prestress and motion state of actual inclined cables illustrated in this thesis into consideration, numerical integration of the nonlinear coupled dynamic equilibrium equation is performed by self-programming according to the deformation compatibility equation established in Chapter 2. The numerical analysis focuses on the mid-span displacement response and the dynamic prestress time response of cables. The numerical results may be used for fatigue design of cable-structures and calculating ultimate load-carrying capacity of cables. Furthermore, the first-order modal frequency, the amplitude of vibration response and the damping influence on cable vibration are also investigated respectively for more useful informations about cable’s nonlinear vibration.At the end of this thesis, some proposals are derived from the nonlinear coupled vibration system. The importance of dynamic prestress varying effect in resonance vibration is emphasized and some future studies in cable dynamic analysis are proposed.更多还原