傾斜纜索的馳振不穩定分析

Abstract

本文首先回顧三種纜索馳振不穩定的形態和其發生原因，以及介紹Glauert-Den Hartog 準則和纜索的馳振臨界風速經驗公式(Saito et al., 1990 )；接著使用桁架元素建立纜索的有限元素模型，並以等效彈性模數及幾何勁度矩陣修正桁架元素使其更符合纜索行為；使用準靜方法推導纜索發生馳振時的外力表示式之後，建立纜索的運動方程式，由於馳振乃是一種自激力振盪行為，因此必須透過狀態空間法，解纜索的特徵值問題，以此求得纜索進入馳振不穩定時的臨界風速。完成數值方法之建立後，透過四個實際的橋梁纜索問題，以驗證本文所提出之數值迭代方法是否可行，同時與纜索的馳振臨界風速經驗公式做一比較；最後進行纜索的參數分析，找出提升纜索穩定度的最有效參數，並逐一討論參數變化所得到的各種結果。

This article is focused on the formulation of a general quasi-steady approach for evaluating the critical wind velocity of cable galloping instability. First, three kinds of cable galloping are introduced, along with two methods for predicting the critical wind velocity of cable galloping instability including the Glauert-Den Hartog criterion and an approximate equation for cable galloping (Saito et al., 1990). Second, a simple cable model with the elastic and geometric stiffness matrices modified by the equivalent modulus of elasticity is used along with a general quasi-steady approach for considering the wind forces. For the self-excited force, i.e., the galloping force, the state-space method is used to solve the eigenvalue problem. Third, the results obtained from the present method are compared with Saito’s approximation for some real examples. Finally, a parametric analysis is conducted to find out the key parameter dominating the cable galloping stability.