【优秀硕博论文】斜拉桥拉索参数振动的理论与数值分析.doc

研究生学位论文
斜拉桥拉索参数振动的理论与数值分析
Theoretical and Numerical Analysis on the Parametric Vibration of Cables in Cable-stayed bridges
申请学位级别工学硕士
专业桥梁与隧道工程
指导教师李永乐教授
二○○九年五月
摘要
斜拉桥是广泛采用的大跨度桥梁形式之一。作为斜拉桥的主要受力构件之一,斜拉索具有大柔度、小质量、小阻尼的特点。拉索易在风荷载或者交通荷载的作用下发生大幅度的参数振动,影响全桥的安全性与耐久性。因此,对斜拉索参数振动进行理论研究与数值分析是非常必要的。
本文首先研究了无垂度张紧弦、小垂度拉索、大垂度拉索动力特性的差别,以及造成差别的原因。然后,分别考虑理想激励和非理想激励建立了拉索的参数振动模型。通过Galerkin方法得出了拉索非线性参数振动微分方程表达式,采用多尺度方法研究了方程中参数激励项、外激励项、非线性项和阻尼对拉索振动特性的影响。采用数值积分方法得出了拉索在外激励作用下发生强迫共振和参数激励下发生参数共振时拉索的响应曲线;建立了拉索面内-面外耦合振动模型,得出了面内-面外耦合振动方程组;采用多尺度方法分析了拉索面内与面外耦合振动的特性,并用数值计算方法得出了3维空间拉索面内-面外发生耦合振动的响应曲线。采用有限元方法,基于ANSYS建立了实际拉索的三维空间的参数振动模型,考虑拉索的应力刚化和几何非线性,对拉索进行了瞬态动力分析。计算结果表明,有限元方法和数值方法计算差别不大。最后,从实际工程出发,建立了实际斜拉桥全桥有限元模型,评估了实际桥梁拉索发生大幅振动的可能性。对实际结构设计中如何考虑减少或避免拉索发生大幅振动的可能性提出了建议。
关键词: 斜拉桥;拉索;参数振动;非线性振动;有限元
Abstract
The long span cable-stayed bridges are widly used for large-span bridges. As the main members to support the weight of the bridge, the stayed cables are prone to voilence vihibit parametric oscillation with large amplitude under the wind or traffic loads due to it’s high flexibility ,low damping and small oscillation can greatly affect the performance of the bridge. In order to improve the design of cable-stayed bridge it is important to study the mechanism of the vibration and perform numerical analysis.
First of all, the dynamic characteristics of the cables with different sags are investigated and the reason which cause the varition are discussed in this dissertation. And then, taking the idealized excitation and nonidealized excitation into consideration, the models of parametric oscillation for cables are built up. The nonlinear oscillation differential equation is got by Galerkin method. According to the equation, the influence of parametric excitation, external excitation, nonlinear terms and damping are investigated  by multiple-scale method. Response curve is obtained for main resonance and parametric resonance by numerical analysis with Runge-Kutta method . In orde