本研究以一非線性 Bernoulli-Euler Beam 為主體模型，將其置放於彈性基底 （Elastic Foundation），此 beam 兩端皆以鉸接 （Hinge） 支撐之。本模式可用以模擬彈性樑置放於任何的彈性基底（Elastic Foundation）之應用，例如鐵公路、橋樑、甚至海底電纜或是輸油管路等。本文使用多尺度法（Method of Multiple Scales, MOMS）分析系統於穩態固定點（Fixed Points）各模態之頻率響應，藉由振幅及振動模態觀察其內共振現象，並以數值法模擬其時間域之振動情形，相互驗證之。本研究將分析連續之移動外力對於非線性彈性樑振動之影響，討論不同的移動外力速度及外力間距對主體系統的影響。為了更全面分析移動外力對系統振幅之影響，將以 ANSYS 軟體模擬與驗證，觀察影響最大之組合。此外，本研究在此系統掛載一動態減振器（Dynamic Vibration Absorber, DVA），分別探討在不同 DVA 之質量、彈性係數以及擺放位置對於主體系統振動之影響，同時找出 DVA 之最佳參數組合，以達到本系統之最佳減振目的。

This study considers a slender nonlinear elastic beam placed on an elastic foundation with a hinge-hinge boundary condition. This model can be used to simulate the vibration motion of elastic beam placed on any elastic foundation, such as railways, bridges, even submarine cables or oil pipelines. We assume that the beam is subjected to an infinite sequence of regularly spaced concentrated moving loads. The combinations of the speeds and distance of the moving load may cause the system with large vibration amplitudes. We employed the method of multiple scales (MOMS) to analyze this nonlinear problem. The Fixed Points plots (steady state frequency response) of each mode were obtained, and that are utilized to examine the internal resonance of the system. The frequency response and the internal resonance are verified by the numerical results in time domain. In order to analyze the effect of successive traveling loads on this system more comprehensively, ANSYS software is used to simulate and verify the cases of the theoretical model. Furthermore, we added a dynamic vibration absorber (DVA) which is suspended under the beam to reduce vibration and prevent internal resonance. DVA with various locations, masses, and spring constants are fully analyzed to find the optimal combination for DVA. These results and findings are presented by tables and plots and are also verified by numerical simulations.

目錄
摘要……………………………………………………………………….I
英文摘要………………………………………………………………...II
目錄……………………………………………………………………..III
表目錄…………………………………………………………………..V
圖目錄…………………………………………………………………..VI
符號說明……………………………………………………………...VIII
第一章	緒論……………………………………………………………..1
1.1  研究動機………………………………………………….1
       1.2  文獻回顧………………………………………………….2
       1.3  研究方法………………………………………………….5
第二章	理論模式之建立………………………………………………..7
2.1  運動方程式之推導……………………………………….7
       2.2  連續之移動外力的理論模式建構………………….……9
       2.3  多尺度法……………………………………………….11
       2.4  彈性樑之模態分析……………………………………...12
第三章	系統內共振之分析……………………………………………15
       3.1  無 DVA 之非線性樑運動方程……………………….15
       3.2  內共振條件之分析……………………………………...15
       3.3  系統頻率響應之分析…………………………………...18
       3.4  內共振現象之驗證……………………………………...24
       3.5  數值法驗證……………………………………………...25
       3.6  ANSYS 模擬驗證………………………………………27
第四章	附加 DVA 之系統分析………………………………………30
4.1 附加 DVA 之理論模式………………………………….30
4.2 系統頻率響應之分析…………………………………….31
第五章	附加DVA之效果與討論……………………………………37
第六章	結論……………………………………………………………40
參考文獻………………………………………………………………..42
附錄（一）系統之各項無因次化參數定義…………………………..44
附錄（二）時間項通解之表示式……………………………………..45
論文簡要版……………………………………………………………..64
 
表目錄
表一 鋼之材料參數……………………………………………………46
表二 附加減振器激擾第一模態之第一模態…………………………46
表三 附加減振器激擾第三模態之第三模態…………………………47

圖目錄
圖1 具減振器之主體架構與邊界條件………….…………………….48
圖2 Freq. Ratio 與 之關係曲線……………………….……………...48
圖3 激擾第一模態之 Fixed Point 圖………………………...………49
圖4 激擾第二模態之 Fixed Point 圖…………………………...……49
圖5 激擾第一模態之 Fixed Point 圖……………………………...…50
圖6 激擾第三模態之 Fixed Point 圖………………………………...50
圖7 激擾第一模態之第一模態 Fixed Point 圖與數值驗證圖……...51
圖8 激擾第二模態之第二模態 Fixed Point 圖與數值驗證圖……...51
圖9 激擾第三模態之第三模態 Fixed Point 圖與數值驗證圖……...52
圖10 橋梁簡化模型…………………..…….………………………….52
圖11 結構分析網格示意圖…………….……………………………...53
圖12 displacement 定義 Hinge…………….………………………….53
圖13 Hinge 設定示意圖……………………………………………….54
圖14 displacement 定義 Roller……………….……………………….54
圖15 Roller 設定示意圖……………………………………………….55
圖16 elastic support 設定示意圖………………………………………55
圖17 最大振幅 vs. 速度和外力間距(無彈性基底)…………………56
圖18 最大振幅 vs. 速度和外力間距(具彈性基底)…………………57
圖19 激擾第一模態之Fixed Point 圖（具減振器）…………………58
圖20 激擾第三模態之Fixed Point 圖（具減振器）…………………58
圖21 激擾第一模態之第一模態（fs=9）…………………………...…59
圖22 激擾第三模態之第三模態（fs=9）…………………………...…60
圖23 mD=0.1之質量塊模型…………………………………………..61
圖24 Spring 設定示意圖………………………………………………61
圖25 彈簧連接主體結構………………………………………………62
圖26 彈簧連接減振器…………………………………………………62
圖27 mD=0.1、lD=0.5、fs=9之模擬結果……………………………63
圖28 mD=0.02、lD=0.25、fs=1之模擬結果…………………………..63
圖29 mD=0.06、lD=0.25、fs=5之模擬結果…………………………..63

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