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 摘 要 本文主旨在研究車輛與不規則表面多重跨距橋樑之動態響應。文中將車體模擬成彈性撓曲樑，將橋樑模擬多重跨距連續的彈性撓曲樑，將假設橋樑為有限長度和均勻斷面的樑，其上不規則輪廓可模擬成為一隨機過程，本文將討論三種型式的路面輪廓，例如白噪音過程、馬可夫過程和平穩高斯過程。 文中利用模態疊加法建立彼此耦合的車輛-橋樑系統之運動方程式。據此，此運動方程式可以化成狀態方程式。最後，利用遞迴演算法求解結構系統之位移平均值和位移變異數，其結果並與蒙地卡羅數位模擬法數值結果作比較，範例中並分別探討懸吊系統阻尼、橋樑長度和車速等參數對系統動態撓曲之影響。
 Abstract This aim of this thesis is to study the dynamic response of the vehicle and the multi-span bridge with irregular surfaces. The vehicle body is modeled as an elastic flexible beam and the bridge is modeled as multi-span continuous elastic flexible beam. The bridge is considered to be a finite length, uniform cross-section beam with an uneven profile, which can be simulated as a random process. Three types of road profiles, such as white noise process, Markov process and the ergodic stationary Gaussian zero mean process, will be discussed in the study. The modal superposition method is used to formulate the equation of motion for the coupled vehicle-bridge system. Accordingly, this equation can be rewritten as a state equation. Finally, the mean value and variance of displacement of the structural system is solved by using the proposed recursive algorithm. The numerical results are compared with those using the Monte Carlo simulation approximation. Examples are presented to study the dynamic deflections with the suspension damping, bridge length and the vehicle velocity respectively, as a parameter.
 目 錄 中文摘要………………………………………………………………… I 英文摘要…………………………………………………………………Ⅱ 誌謝………………………………………………………………………Ⅲ 目錄………………………………………………………………………Ⅳ 符號所引………………………………………………………………..Ⅴ 圖表索引………………………………………………………………..Ⅷ 第一章 緒論………………………………………………………….…1 1.1 前言………………………………………………………………1 1.2 文獻回顧…………………………………………………………2 1.3 本文目的與架構…………………………………………………7 第二章 車體樑及連續樑之模態分析………………………………….9 2.1 數學模式…………………………………………………………9 2.2 撓性車體樑模態分析………………………………………….11 2.3 多重跨距連續橋樑模態分析………………………………….14 第三章 車輛-橋樑系統之運動方程式……………………………….19 3.1 車體樑運動方程式…………………………………………….19 3.2 橋樑運動方程式……………………………………………….20 3.3 振動系統運動方程式………………………………………….22 第四章 振動隨機響應分析..………………………………………..26 4.1 響應關聯方程式……………………………………………….26 4.2 遞迴法………………………………………………………...29 4.3 數位模擬法…………………………………………………….33 第五章 數值範例和討論………………………………………………35 5.1系統參數….…………………………………………………...35 5.2自然振動模態.………………………………………………...36 5.3 數值範例一 平均值……………………………………………39 5.4 數值範例二 白噪音過程………………………………………48 5.5 數值範例三 一階馬可夫過程…………………………………56 5.6 數值範例四 平穩高斯過程………….……………………….65 5.7 數值範例五 二跨距連續橋樑……….……………………….74 第六章 結論與未來展望……………………………………………..91 參考文獻……………………………………………………………...93 附錄…………………………………………………………………….97 作者簡介……………………………………………………………….100 授權書………………………………………………………………….101