计入重力弦向分量影响的斜拉索非线性自由振动分析

袁从森,沈锐利,周凌远,李伟东,官快

振动与冲击 ›› 2015, Vol. 34 ›› Issue (12) : 201-206.

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (12) : 201-206.
论文

计入重力弦向分量影响的斜拉索非线性自由振动分析

  • 袁从森,沈锐利,周凌远,李伟东,官快
作者信息 +

The Nonlinear Free Vibration of Inclined Cables Taking into Account the Effect of the Chord Component of the Gravity

  • Yuan Cong-sen, Shen Rui-li, Zhou Ling-yuan, Li Wei-dong,GUAN Kuai
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文章历史 +

摘要

为了进一步准确计算斜拉索的自振频率,考虑斜拉索的重力在弦向的分量对斜拉索非线性振动的影响,分别建立了斜拉索的垂度微分方程和非线性自由振动方程,采用幂级数法求解垂度微分方程,采用伽辽金法把偏微分方程转化为常微分方程,运用摄动法求得该方程的近似解,并制定了相应的数值计算方法,与理论解进行了比较。研究了考虑索力变化影响后拉索的振动特性,采用了更精确的函数来逼近垂度悬链线,解决了考虑重力在弦向的分量时,用抛物线来逼近垂度悬链线时的精度不足的问题。随着索的长度增加,索的总质量也越来越大,因此要考虑斜拉索的重力弦向的分量对斜拉索的振动的影响。

Abstract

Taking into account the effect of the chord component of the gravity in the nonlinear free vibration of inclined cables, the nonlinear equations of motion for an inclined cable were developed. The sag differential equation and nonlinear free vibration equation of the sag are established, and the sag differential equation is solved with the method of power series. Galerkin’s method was used to convert the nonlinear partial differential equations into ordinary differential equations. The approximate solution of the equations was obtained with perturbation method. The corresponding numerical method was developed and compared with theoretical solution. Vibration characteristic of inclined cables is studied considering the change of forces. A more precise function was chosen to approximate the catenary sag, which is more precise than the parabola. Total mass of inclined cable increases with the increasing of the length, so the effect of the chord component of the gravity on the vibration of inclined cables must be considered.

关键词

斜拉桥 / 斜拉索 / 非线性振动 / 弦向分量

Key words

Cable Stayed Bridges / Inclined Cables / Nonlinear Vibration / Chord Component

引用本文

导出引用
袁从森,沈锐利,周凌远,李伟东,官快. 计入重力弦向分量影响的斜拉索非线性自由振动分析[J]. 振动与冲击, 2015, 34(12): 201-206
Yuan Cong-sen, Shen Rui-li, Zhou Ling-yuan, Li Wei-dong,GUAN Kuai. The Nonlinear Free Vibration of Inclined Cables Taking into Account the Effect of the Chord Component of the Gravity[J]. Journal of Vibration and Shock, 2015, 34(12): 201-206

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