姜  健，李国强
(同济大学，上海200092)

[摘要] 本文主要研究了拉索振动的轴向被动控制。在拉索端部沿轴向设置弹性约束，通过影响索端支座的移动，从而改变拉索的振动特性，最终达到减振效果。考虑垂度、几何非线性及抗弯刚度的影响，通过D'Alembert原理建立拉索-约束系统平面内横向振动方程，通过Galerkin方法将偏微分方程转化为常微分方程，应用龙格-库塔数值积分法求解方程；经过仿真分析，验证了该振动控制具有明显的减振效果，并且讨论了垂度、初始拉力、横截面积、索长及弹簧刚度对减振效果的影响；最后给出了计算最优阻尼系数的近似解析式，为工程师提供了简便有效的参考依据及设计方法。
[关键词] 拉索振动；轴向被动控制；D'Alembert原理；Galerkin方法；龙格-库塔积分；最优阻尼系数；近似解析式

    Theoretical Study on Vibration Control of Cables with Elastic End Restraint
    Jiang Jian, Li Guoqiang
    ( Tongji University, Shanghai 200092, China)

Abstract: This paper mainly studies the axial passive control of tensile cable vibrations. An elastic restraint is set at the end of cable in axial direction and the support translation is influenced which accordingly leads to the change of vibration characteristics of cable and the damping effects are arrived at eventually. Taking the sag, geometric non-linearity and bending stiffness into account, the governing equation of in-plane vibration of cable-restraint system is established by means of D'Alembert principle, and then those partial differential equations are transformed into a set of ordinary differential equations through Carlerkin method. The method of Runge-Kutta integration is applied to solve the equation. The simulation analysis is processed to prove that this vibration control has obvious damping effects and then the influence of the sag, initial tension, cross sectional area, length and spring rigidity on the damping effects are discussed. Eventually, the approximate analytic solution of the optimum damping coefficient is obtained in order to provide a simple and effective reference and design method for the engineers.
Keywords: cable; axial passive control; D'Alembert principle; Carlerkin method; Runge-Kutta integration; optimum damping coefficient; approximate analytic solution