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Title: | 車橋互制系統之頻率和能量分析:考慮多懸浮質量對簡支橋影響 Frequency and Energy Analysis of Vehicle-Bridge Interaction System: Considering the Effect of Multiple Sprung Masses on Simply Supported Bridge |
Authors: | 鄭棋 Chi Cheng |
Advisor: | 張家銘 Chia-Ming Chang |
Keyword: | 橋梁工程,車橋互制系統,頻率響應函數,狀態空間法,有限元素法, Bridge Engineering,Vehicle-Bridge Interaction System,Frequency Response Function,State-Space Method,Finite Element Method, |
Publication Year : | 2023 |
Degree: | 碩士 |
Abstract: | 當車輛行駛於橋梁上時,車輛和橋梁之間產生的互制力是系統主要動力反應 來源。若橋梁、車輛及外力的頻率和能量達到一定範圍,可能造成橋梁變形過大, 進而造成橋梁損壞、車輛失控或其他安全問題。因此,了解車橋互制系統的特性 和行為,可以幫助我們規劃更安全、高效的交通運輸系統,同時也有助於我們設 計更耐用的橋梁和車輛載具。
關於車橋互制系統的頻率分析,目前的研究主要是以車輛掃描法(vehicle scanning method)進行橋梁頻率的間接量測。該方法利用車輛與橋梁之間的互制特 性,以車輛的垂直加速度反應進行頻率分析,提取出隱含的橋梁頻率,將測得的 橋梁頻率與過去的橋梁頻率進行比較,可以作為結構健康監測的工具。然而,車 輛掃描法目前還無法透過改變結構系統的參數來討論各參數對車橋互制系統能量 與頻率的影響。雖已有研究提出車橋互制系統瞬時頻率解析解,但該解析解尚無 法用於討論能量變化。因此,本研究基於上述的瞬時頻率解析解研究基礎,進一 步計算車橋互制系統的瞬時頻率響應函數。這不僅可以觀察車輛通過橋梁時的瞬 時頻率,還可以瞭解該瞬時頻率隱含的能量大小,幫助工程師在設計橋梁時,選 擇更有效率的設計方法,或在橋梁結構健康監測中,決定需要優先檢查的地點。 本研究首先進行車橋互制反應之理論解推導,以單一懸浮質量或多懸浮質量 模擬行徑中之列車,應用假設模態法以第一模態或多模態疊加之方式模擬橋梁反 應,據此建立車橋互制運動方程式。接著應用拉普拉斯轉換,藉由車輛運動方程 式找到頻率域車輛位移與橋梁位移之變數變換關係,得到動態濃縮後的整體系統 運動方程式,並據以解算車橋互制系統之瞬時頻率響應函數。此外,本研究也以 Yang and Yau 所提出之車橋互制元素建立數值模型,應用狀態空間法對數值模型 進行頻率域分析,藉此得到系統瞬時頻譜圖。最後,本研究將解析解與數值模型 所得之瞬時頻譜圖進行比較,完成本研究瞬時頻率響應函數之理論驗證。 When vehicles travel on bridges, there is interaction between the vehicles and the bridges. This interaction serves as the primary external force acting on the bridge during operation. If the frequency and energy of the external force reach a certain range, it may lead to bridge damage, vehicle instability, or other safety issues. Therefore, understanding the characteristics and behavior of the vehicle-bridge interaction system can help us design safer and more efficient transportation systems or design more durable bridges and vehicles. Current research mainly focuses on the vehicle scanning method regarding the frequency analysis of the vehicle-bridge interaction system. This method utilizes the interaction characteristics between vehicles and bridges to analyze the frequencies by examining the vehicle's acceleration response and extracting the bridge frequencies. The measured bridge frequencies are then compared with the historical bridge frequencies, serving as a tool for structural health monitoring. However, the vehicle scanning method currently cannot analyze the effects of varying structural system parameters on the energy and frequencies of the vehicle-bridge interaction system. Although some studies have proposed analytical solutions for the instantaneous frequencies of the vehicle's response, these solutions cannot be directly used to discuss energy variations. Therefore, based on the aforementioned analytical solutions for instantaneous frequencies, this study further calculates the instantaneous frequency response function of the vehicle-bridge interaction system. This not only allows us to observe the instantaneous frequencies when a vehicle passes over a bridge but also provides insights into the energy associated with those instantaneous frequencies. This is beneficial for engineers in selecting more efficient structural design methods for bridges or determining priority inspection locations in bridge structural health monitoring. In this study, theoretical derivations of the vehicle-bridge interaction response are first conducted. The moving train is simulated using a single sprung mass or multiple sprung masses, and the bridge is modeled using the assumed mode method with the first mode or a superposition of multiple modes. Based on this, the equation of motion for the vehicle-bridge interaction system with two subsystems are established. Then, by applyingLaplace transforms and utilizing the vehicle equation of motion, the relationship between the frequency domain vehicle displacement and bridge displacement is derived. The overall system equation of motion after dynamic condensation are obtained, and subsequently, the instantaneous frequency response function of the vehicle-bridge interaction system is solved. Additionally, the numerical model based on the vehicle- bridge interaction elements proposed by Yang and Yau is established, and frequency domain analysis of the numerical model is conducted using the state-space method to obtain the system's instantaneous frequency spectrum. Finally, a comparison is made between the instantaneous frequency spectra obtained from the analytical solution and the numerical model, completing the theoretical validation of the instantaneous frequency response function in this study. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/90658 |
DOI: | 10.6342/NTU202303667 |
Fulltext Rights: | 同意授權(限校園內公開) |
Appears in Collections: | 土木工程學系 |
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