頁籤選單縮合
題 名 | 車輛-橋樑動力互制問題的有限元素求解方法研究=A Study on FEM Analysis Procedures of Vehicle-Bridge Dynamic Interaction Problems |
---|---|
作 者 | 楊佳螢; 李洋傑; 林聰悟; | 書刊名 | 應用聲學與振動學刊 |
卷 期 | 3:1 2011.04[民100.04] |
頁 次 | 頁1-12 |
分類號 | 441.8 |
關鍵詞 | 車橋互制; 移動載重; 模態分析; Vehicle-Bridge interaction; Moving load; Modal reduction method; |
語 文 | 中文(Chinese) |
中文摘要 | 本文之研究標的為車輛-橋樑的動力互制問題,求解過程中路面不平整之效應也會納入考慮。求解的入手進路為時間域有限元素法,首先,利用有限元素法分別為車輛與橋樑建立運動方程式,在組合完成之兩組運動方程式中,車輛-橋樑間的動態互制力先作為未知量。其次,對橋體之運動方程式進行模態分析,並利用所得模態簡併橋體之運動方程式,改寫為使用橋體模態廣義位移之表示式。再者,利用車輪節點與橋體有限元素上之接觸點的變位一致關係,消去所有未知動態互制力,推導出車輛-橋樑動力互制分析的耦合運動方程式;由於上述接觸點會隨時間連續變化,本文也對接觸點位於橋體有限元素內部而非節點上之情形進行合乎有限元素形狀函數之處理。最後,也進一步對車輛做模態分析,並利用其所得模態再度進行模態簡併,推導出完全使用車輛與橋樑兩個系統之模態廣義位移的耦合方程式。耦合運動方程式(為一個係數為時間相關的二階常微分方程組)之時域積分,再改寫為一階常微分方程組後,利用Runge-Kutta法求解。為驗證本文所提數值分析方法的精確性,本文也針對數種可以利用偏微分方程進行解析解法的案例,利用本文所提數值分析方法求出數值解,所得結果與解析解的比對皆相當吻合。另外本文也針對兩種前人研究所計算過的案例,以所提數值分析方法進行數值計算,所得結果與前人研究結果的比對也相當吻合。 |
英文摘要 | In this article, we are aiming at a study on a typical vehicle-bridge dynamic interaction problem in which uneven road surface profile can be considered. The objective is a time-domain FEM analysis procedure for the numerical calculations of the dynamic responses of a vehicle-bridge system while the vehicle moves along the surface of this bridge. The FEM formulation can be divided into 5 stages: (1) By using standard FEM procedure, the matrix equations of motions are constructed for both of the vehicle and bridge systems, in which the dynamic interaction forces are temporary unknown quantities. (2) By using the modal shapes of the bridge system, a modal-reduction procedure is performed on the equations of motions of the bridge system. (3) By using the compatibility equations of the displacements at the contact points between the vehicle and the bridge, the unknown interaction forces are eliminated to obtain coupled equations of motions for the vehicle-bridge system. (4) By using the modal shapes for the whole vehicle system, further modal-reduction procedure is performed on the coupled equations of motions of the whole system. (5) Runge-Kutta numerical scheme is used for the time-stepping solution of the coupled equations of motions which are constructed in the stage (4). In order to validate the numerical procedure proposed, several simplified cases, analytical solutions of which can be obtained, are studied. The numerical results obtained seem to be quite satisfactory as being compared with analytical solutions. Further more, two cases which are studied by previous research are analyzed by using the numerical procedure proposed, numerical results obtained are quite satisfactory as being compared with results obtained by previous research. |
本系統中英文摘要資訊取自各篇刊載內容。