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姜  健，李國強(qiáng)
(同濟(jì)大學(xué)，上海200092)

[摘要] 本文主要研究了拉索振動(dòng)的軸向被動(dòng)控制。在拉索端部沿軸向設(shè)置彈性約束，通過影響索端支座的移動(dòng)，從而改變拉索的振動(dòng)特性，最終達(dá)到減振效果?？紤]垂度、幾何非線性及抗彎剛度的影響，通過D'Alembert原理建立拉索-約束系統(tǒng)平面內(nèi)橫向振動(dòng)方程，通過Galerkin方法將偏微分方程轉(zhuǎn)化為常微分方程，應(yīng)用龍格-庫塔數(shù)值積分法求解方程；經(jīng)過仿真分析，驗(yàn)證了該振動(dòng)控制具有明顯的減振效果，并且討論了垂度、初始拉力、橫截面積、索長及彈簧剛度對(duì)減振效果的影響；最后給出了計(jì)算最優(yōu)阻尼系數(shù)的近似解析式，為工程師提供了簡便有效的參考依據(jù)及設(shè)計(jì)方法。
[關(guān)鍵詞] 拉索振動(dòng)；軸向被動(dòng)控制；D'Alembert原理；Galerkin方法；龍格-庫塔積分；最優(yōu)阻尼系數(shù)；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