臺灣博碩士論文加值系統

本文以分析結構樑的模態形狀與自然頻率為主，以二根自由結構樑中間搭配數根耦合樑建立一套傳遞外力的數學模型，以推導結構系統振動樑的運動方程式與有限元素分析(Finite Element Analysis)搭配，研究結構樑的振動行為，並驗證其數學模型相對應的模態形狀與自然頻率。本文中介紹進行模態分析所需應用之數學理論，如：扭轉振動理論、多自由度振動系統、漢米爾頓原理、假設模態法等...。首先探討一具自由邊界條件的結構樑，中間加入不同數目的支承或耦合樑，探討側向模態的變化情形，進而加入外力刺激可藉由耦合樑將振動源傳遞至第二根樑上可推得系統的數學模型並可求解出系統的振動位移及加速度，透過耦合樑位置或結構尺寸調整可設計一個降低振動量與加速度的雙根耦合自由樑系統，避開模型的共振頻率，以達到減振的效果。本研究將此雙根耦合自由樑應用於工程分析的數學模型，以ANSYS模擬二輪車排氣管後叉連接系統之模型做驗證，利用扭轉振動理論與假設模態法可快速且準確得到此系統模型的自然頻率與加速度。研究結果發現，移動耦合樑位置對此系統模型加速度得到3%的改善，貢獻度並不大，但與理論預測相符合，本研究建議提高固定點耦合樑的彈性系數或降低系統模型的轉動慣量可大幅改善此系統加速度的方法，此設計方法可應用在工程結構的機械振動分析、減振分析、振動控制及動、靜態分析。

This work aims at analyzing the mode shape and natural frequency of structural beams, using two free beams and many coupling beams to build a mathematical model that transfers forces. With this mathematical model, the equation of motion of structural system vibrating beam can be derived, and Finite Element Analysis is employed as reference to further study the vibrating behavior of structural beam and to verify the mathematical model in terms of its mode shape and natural frequency. This work introduces the mathematical theory applied to mode analysis, including torsional vibration theory, multiple degree of freedom system , and Hamilton theory, assume mode method. To begin with, a beam with free boundary condition is analyzed, and then different numbers of bearings and coupling beams are added to investigate the changes of lateral mode. Additionally, upon the external stimuli added, it proves that vibrating source can be transferred to the second beam by coupling beams so as to derive system’s mathematical model and its vibration displacement and acceleration. With the displacement and size adjustment of coupling beams, two coupled free-free beam with the ability to lower the vibration and acceleration can be produced for successful vibration damping and avoidance of resonance frequency of the model. This two coupled free-free beam can also be applied to the mathematical model for engineering analysis. In order to verify Fork Connection System of motorcycle exhaust pipes, this work employs torsional vibration and assume mode method to quickly and precisely obtain its natural frequency and acceleration, while ANSYS is traditionally used as simulation to verify the mathematical model. The research results show insignificant 3% of improvement to acceleration due to the displacement of coupling beams, but the result matches the theory results. This work suggests the rise of Elasticity Coefficients at fixed points or the drop of Moment of Inertia of system model should be needed to improve the acceleration of system. In terms of engineering structure, this design method is applicable and effective to mechanical vibration analysis, damping analysis, vibration control, dynamic analysis and static analysis.

摘要 II
Abstract III
誌謝 V
目錄 VI
圖目錄 IX
表目錄 XII
符號說明 XIII
第一章 緒論 1
1-1 研究動機 1
1-2 文獻回顧 2
1-3 研究目的 11
1-4 本文貢獻 14
1-5 本文大綱 15
第二章 雙根耦合自由樑理論推導與模擬 16
2-1 連續樑理論 16
2-2 雙根耦合自由樑分析流程架構 20
2-3 不同支撐條件連續樑之振動響應分析 23
2-3-1 懸臂樑模態分析與頻率響應分析 23
2-3-2 簡支承懸臂樑模態分析與頻率響應分析 25
2-3-3 簡支樑模態分析與頻率響應分析 28
2-3-4 具二支撐彈簧連續樑的模態分析與頻率響應分析 31
2-3-5 連續樑模態函數的理論推導 35
2-3-6 樑的側向強制振動分析 39
2-4 ANSYS軟體模擬雙根耦合自由樑之模態與自然頻率 42
2-4-1 雙根耦合自由樑尺寸材料參數 43
2-4-2 ANSYS模擬條件設定與收斂性分析 45
2-4-3 剛性扭轉振動原理探討雙根耦合自由樑剛性模態 49
2-4-4 漢米爾頓原理探討雙根耦合自由樑側向模態 51
2-4-5 雙根耦合自由樑其他模態分析 56
第三章 單根樑與雙根樑系統理論結果與分析 60
3-1 單根樑在不同邊界條件下的模態與頻率響應分析 60
3-1-1 以MATLAB軟體模擬懸臂樑之模態函數與自然頻率 60
3-1-2 以MATLAB軟體模擬簡支承懸臂樑之模態函數與自然頻率 62
3-1-3 以MATLAB軟體模擬簡支樑之模態函數與自然頻率 64
3-1-4 以MATLAB軟體模擬二支撐彈簧連續樑之模態與自然頻率 66
3-2 雙根耦合自由樑理論之自然頻率結果分析 68
3-2-1 扭轉振動模態理論分析與ANSYS模擬結果比較 68
3-2-2 撓曲側向模態理論分析與ANSYS模擬結果比較 69
3-2-3 其他模態理論分析與ANSYS模擬結果比較 74
3-2-4 雙根耦合自由樑理論與模擬之自然頻率結果比較 79
第四章 雙根耦合自由樑模型之減振實例應用 83
4-1 二輪車數學模型之建立 83
4-2 多根耦合自由樑應用於二輪車減振模型 85
4-3 調整耦合樑位置之減振成效比較 98
第五章 結論與未來展望 107
5-1 結論 107
5-2 未來展望 108
參考文獻 109

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