温度变化对悬索全局动力学特性影响

Influences of Temperature Changes on Global Dynamical Characteristics of Suspended Cables

索是一类工程中常用的张力结构,其柔度大、阻尼轻,在各类外部荷载作用或端部位移激励下极易发生大幅振动,影响结构安全运营.已有研究表明悬索的振动特性对于温度变化极为敏感,因此本文同时考虑支座运动引起的参数共振以及模态间1∶2内共振,基于全局分岔理论,系统探究温度变化对悬索全局动力学行为的影响.首先引入张力改变系数,建立考虑整体温度变化影响与受参数激励悬索的面内非线性运动微分方程.采用Galerkin法进行离散,利用多尺度法得到该非线性系统直角坐标形式的平均方程,并基于坐标变换,将平均方程简化为规范形,采用能量相位法研究温度变化时悬索多脉冲混沌动力学行为.通过能量差函数的零点条件以及扰动系统下中心点的吸引域范围,分析激励幅值、阻尼系数和调谐参数的取值范围,并计算该四维系统的Lyapunov指数.研究结果表明:温度变化会影响系统Shilnikov型多脉冲同宿轨道的产生;随着温度变化,多脉冲同宿轨道可能消失,导致系统的混沌运动转变为周期运动;受温度变化影响,动力系统可能展现出截然不同的动力学行为.

The suspended cable is a type pf commonly used tension structure in engineering structures.It has high flexibility and light damping,and it is prone to large vibrations under various excitations and/or support motions,which endangers the safety of the cable structures.The previous studies have shown that the vibration characteristics of the dynamic system are very sensitive to temperature changes.Therefore,this paper considers both the parametric resonances caused by the support motions and the two-to-one internal resonances,and then it systematically explores the influences of temperature changes on the suspended cable’s dynamic behaviors from the perspective of global bifurcations.Firstly,the tension variation coefficient is introduced,and the nonlinear differential equations of the in-plane motion of the suspended cable subjected to parametric excitation in thermal environments is established.The Galerkin method is used for discretization,and the multiple scales method is adopted to obtain the average equation of the nonlinear system in rectangular coordinates.Based on the coordinate transformation,the average equation is simplified into a normal form.The energy phase method is used to explore the multi-pulse chaotic dynamical behavior of the suspended cable when the temperature is changed.Through the zero-point condition of the energy-difference function and the range of attraction of the center point under the disturbance system,the excitation amplitude,damping coefficient and detuning parameters of the system are explored,and the Lyapunov exponents of the four-dimensional system are calculated.Numerical examples show that:temperature changes affect the generation of system’s Shilnikov-type multi-pulse orbits.The multi-pulse orbits may disappear considering temperature effects,and it causes the system’s chaotic motions transform into periodic motions.The dynamical system may exhibit distinct vibration behaviors in thermal environments.