臺灣博碩士論文加值系統

本文探討樑結構系統於簡諧外力激振狀態下之模態分析，發展由操作變形振型求模態振型之預測模式。分別針對簡支樑與懸臂樑進行理論模式推導，利用數值模擬分析的方式來驗證由操作變形振型求模態振型的理論預測模式的可行性，成功的預測出模態振型，經由簡諧分析得知操作變形振型是由模態參數所組成的函數，其中自然頻率與阻尼比可經由一次頻率響應函數量測得知，本文利用懸臂樑於共振及非共振激振狀態下量測所得之操作變形振型，均能合理地預測出樑結構之模態振型，本研究將有助於作業狀態下結構之模態分析，將可運用於操作狀態下的轉子系統。

This work presents modal analysis of beam structure in operating conditions. In particular structure is in the harmonic excitation. the prediction model is developed to determine mode shapes from operational deflection shape (ODS). Both simply supported beam and cantilever beam are considered. Numerical simulation is performed to show the feasibility of the developed prediction model. Mode shapes can be well predicted. The harmonic response analysis is first presented. The ODS can be shown as function of modal parameters. Natural frequencies and damping ratios can be obtained from single measurement of frequency response function. Therefore, Experimental verification is also conducted for a cantilever beam. The ODS of beam is first measured for both on-resonance and off- resonance excitation cases. The prediction model can then employed to determine structure mode shapes. Results show that predicted mode shapes reasonably agree with the theoretical mode shapes. The developed methodology will be beneficial for structure modal analysis in operating condition. In Particular, This developed prediction model can be applied to rotor system in its operating condition.

目 錄
摘要………………………………………………………….……Ⅰ
英文摘要……………………………………………………….…Ⅱ
誌謝……………………………………………………………….Ⅲ
目錄…………………………………………………………….…Ⅳ
圖目錄…………………………………………………….….…Ⅵ
表目錄……………………………………………..……….……Ⅷ
第一章 緒論………………………………………..………..….....1
1.1 研究動機…………………………………..………….…..1
1.2 文獻回顧……………………………………………..…..2
1.3 全文概述……………………………………..….….…….5
第二章 理論分析…………………………………………..……...7
2.1 自由振動分析………………………………………..…...7
2.1.1共振激振下之預測結果………..…….……………8
2.1.2非共振激振下之預測結果……………...…….….10
2.2 簡諧分析…………………………………..……….....…12
2.3 操作變形振型求模態振型分析….………………..……16
2.4 結論……………………..…………………………........21
第三章 數值模擬分析……………………………………….…..22
3.1 預測程式的發展……………………………………...…22
3.2 簡支樑之驗證分析…………….……….…………..…...25
3.2.1共振激振下之預測結果………..…….……………26
3.2.2非共振激振下之預測結果……………...…….….34
3.3懸臂樑之驗證分析……………………………………...41
3.3.1共振激振下之預測結果……………………..……42
3.3.2非共振激振下之預測結果…………….……...50
3.4結論………………………………………..……………...57
第四章 實驗分析…………………………………………..…….58
4.1 懸臂樑模型驗證……………….……..……....……....…58
4.1.1頻率響應函數分析……………….……….....….…61
4.1.2模態參數分析………………………………...……61
4.2 操作變形振型量測………………..………...…….….…64
4.2.1量測方法…………………………………..…….…65
4.2.2量測結果………………………..……..……...……69
4.3 操作變形振型預測模態振型………….…..…..…...…..75
4.3.1共振激振下之預測結果………………….…..……75
4.3.2非共振激振下之預測結果…………..…..…..……93
4.4 結論………………………………………………..…...111
第五章 結論與建議…………………………………….………112
5.1 結論…………..…………………………..………….…112
5.2 建議………..………………………………………...…114
參考文獻…………………………….……………………..……115
圖 目 錄
圖2-1簡支樑、懸臂樑尺寸之簡諧外力作用位置圖………...….12
圖2-2模態振型預測示意圖…………………...….……….….…16
圖2-3 振型多項式函數嵌合示意圖……...….…..……..…17
圖2-4模態振型 示意圖…………………..………...…………18
圖2-5操作變形振型預測模態振型流程圖.…………….………20
圖3-1程式發展流程圖…………….………………….…………24
圖3-2簡支樑理論模態振型………………..……..……………..26
圖3-3 =32.2509Hz之ODS比較與預測模態振型圖……28
圖3-4 =129.0038Hz之ODS比較與預測模態振型圖…28
圖3-5 =290.2585Hz之ODS比較與預測模態振型圖…29
圖3-6目標函數收斂圖……………………………………...…...29
圖3-7 =77Hz之ODS比較與預測模態振型圖.…..…...35
圖3-8 =215Hz之ODS比較與預測模態振型圖…..…...36
圖3-9 =400Hz之ODS比較與預測模態振型圖…..……36
圖3-10懸臂樑理論模態振型………………………..…………..42
圖3-11 =14.272Hz之ODS比較與預測模態振型圖…….44
圖3-12 =92.298Hz之ODS比較與預測模態振型圖..…..45
圖3-13 =258.43Hz之ODS比較與預測模態振型圖……45
圖3-14 =57Hz之ODS比較與預測模態振型圖……….51
圖3-15 =176Hz之ODS比較與預測模態振型圖………52
圖3-16 =368Hz之ODS比較與預測模態振型圖………52
圖4-1懸臂樑模型及量測分割圖……………………………..…59
圖4-2實驗儀器架構圖…………………………………………..60
圖4-3實驗與理論頻率響應函數比較圖………………………..62
圖4-4理論與實驗振型比較圖…………………………………..62
圖4-5時域法之ODS量測訊號圖…………………………….…66
圖4-6頻域法之ODS量測訊號圖…………………………….…67
圖4-7 ODS示意圖……………………………………………….68
圖4-8 ODS量測實驗架構圖……………..……………………...70
圖4-9共振激振下之ODS比較圖…………………………….…71
圖4-10非共振激振下之ODS比較圖…………………………..73
圖4-11 14 實驗與預測ODS比較圖……………....…82
圖4-12 14 實驗ODS預測模態振型比較圖..…….….82
圖4-13 90 實驗與預測ODS比較圖…………..…….87
圖4-14 90 實驗ODS預測模態振型比較圖……….…87
圖4-15 253 實驗與預測ODS比較圖……….………..92
圖4-16 253 實驗ODS預測模態振型比較圖….……..92
圖4-17 =57Hz 實驗與預測ODS比較圖…..…100
圖4-18 =57Hz 實驗ODS預測模態振型比較圖…
…….….…………………………………………………..100
圖4-19 =176Hz 實驗與預測ODS比較圖…...105
圖4-20 =176Hz 實驗ODS預測模態振型比較圖..
………………………………………………………..…105
圖4-21 =368Hz 實驗與預測ODS比較圖…...110
圖4-22 =368Hz 實驗ODS預測模態振型比較圖..
…………………………………………………………..110
表 目 錄
表3-1簡支樑幾何尺寸及材料性質表…………………………..25
表3-2共振激振之理論ODS與預測ODS結果比較……………30
表3-3預測與理論模態振型之MAC與MSF（ =32.2509 Hz）
……………………………………………………………..33
表3-4預測與理論模態振型之MAC與MSF （ =129.0038 Hz）………………………………………………………33
表3-5預測與理論模態振型之MAC與MSF（ =290.2585 Hz）
………………………………..……………………………33
表3-6非共振激振之理論ODS與預測ODS結果比較…………37
表3-7預測與理論模態振型之MAC與MSF（ =77Hz）..…40
表3-8預測與理論模態振型之MAC與MSF（ =215Hz）.40
表3-9預測與理論模態振型之MAC與MSF（ =400Hz）..40
表3-10懸臂樑幾何尺寸及材料性質表………………………….41
表3-11共振激振之理論ODS與預測ODS結果比較…………..46
表3-12預測與理論模態振型之MAC與MSF（ =14.272Hz）
……………………………………………………………49
表3-13預測與理論模態振型之MAC與MSF（ =92.298Hz）
……………………………………………………………49
表3-14預測與理論模態振型之MAC與MSF（ =258Hz）..49
表3-15非共振激振之理論ODS與預測ODS結果比較………..53
表3-16預測與理論模態振型之MAC與MSF（ =57Hz）
……………………………………………………………56
表3-17預測與理論模態振型之MAC與MSF（ =176 Hz）
……………………………………………………………56
表3-18預測與理論模態振型之MAC與MSF（ =368Hz）
……………………………………………………………56
表4-1懸臂樑之尺寸與材料性質………………………..………59
表4-2理論與實驗分析前四個自然頻率及誤差百分比…..……63
表4-3實驗與修正後前四個模態阻尼比………………………..63
表4-4實驗振型與理論振型之模態保證指標…………………..64
表4-5 14 實驗ODS預測模態振型結果…………..…78
表4-6 90 實驗ODS預測模態振型結果……………...83
表4-7 253 實驗ODS預測模態振型結果…………….88
表4-8 =57Hz 實驗ODS預測模態振型結果..…96
表4-9 =176Hz 實驗ODS預測模態振型結果..101
表4-10 =368 Hz 實驗ODS預測模態振型結果
………………………………………………………….106

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