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研究生:蔡盈安
研究生(外文):Ying-An Tsai
論文名稱:虛擬模態振形法之理論與實驗驗證
論文名稱(外文):On the Theory and Experimental Validation of Pseudo Mode Shape Method
指導教授:楊大中楊大中引用關係
學位類別:碩士
校院名稱:元智大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2010
畢業學年度:99
語文別:中文
論文頁數:187
中文關鍵詞:模型凝縮子結構頻率響應函數有限元素法剛體模態多接點基座
外文關鍵詞:Model reductionSubstructureFrequency response functionFinite element methodRigid body modeMultiple jointFoundation
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大型產業機械基座之結構相當複雜,導致模態實驗與有限元素法建模之困難及分析上之不便。現場進行模態測試時,不易取得完整的模態;有限元素法分析,常因結構大型且複雜,不易建模,並因元素過多造成計算費時。
虛擬模態振形法僅需在子結構與母結構接點處施力,量測其頻率響應函數(FRF)。以推導出子結構之等效質量、阻尼和勁度矩陣。由於僅需量測接點處的FRF,因此實驗過程可簡化許多。可有效解決大型複雜結構,無法進行完整模態測試的缺點,同時可以涵蓋頻寬內之所有模態。
本文首先探討虛擬模態振形法之理論,並證明本法之建模精準度與MRM相同。深入探討虛擬質量、阻尼和勁度矩陣之意義,所對應之模態向量之正確性,本方法之可行性及誤差來源。
接著本文以2D的樑結構為範例進行模擬,驗證本理論之建模精準度。並推導子結構之剛體模態和多接點子結構之應用。最後並以實驗驗證其可行性。
最後本文以轉子-軸承-基座系統實驗證虛擬模態振形法應用於基座結構建模上。本文第四章視基座為子結構,以虛擬模態振形法建模。視轉子部分為母結構,以3D Timoshenko beam元素建模。並討論虛擬模態振形法剛體模態之效應與其推導過程。


The foundations of most large industrial machines are complicated in configuration and shape that results in difficulty of modal testing and/or finite element modeling. Modal testing suffers from incomplete measurement of mode shapes, whereas, finite element method faces the problems of the complexity of structural configuration and computational time consuming due to huge amount of elements.
Pseudo Mode Shape Method (PMSM) needs only the measurement of frequency response functions at the joints of the substructure and the mother structure to derive the equivalent mass, damping, and stiffness matrices of the substructure, which greatly simplifies the modeling procedure of the complicated substructure. The established matrices can cover all the modes in the interested frequency range.
In this paper, theoretical aspects of the pseudo mode shape method were remarked. This method was validated to have the same modeling accuracy as Modal Reduction Method (MRM). The meanings of the resulted equivalent mass, damping, and stiffness matrices, as well as the corresponding modal vectors were clarified. Moreover, the feasibility and error sources of PMSM were discussed.
A 2-D beam is used to demonstrate the usage and modeling accuracy of this method. The substructures include rigid body modes and involve multiple joints with the mother structure. The effectiveness of these extensions was validated by experiment.
Experimental validation of PMSM was conducted by modeling the foundation of a rotor-bearing-foundation system. The foundation is treated as the substructure and modeled by PMSM. The rotor is treated as the mother structure and modeled by finite element method using 3D Timoshenko beam elements. The derivation and the effects of rigid body modes of PMSM in this experiment are also investigated.


第一章 、緒論 1
1.1 前言 1
1.2 文獻回顧 3
1.3 研究動機及目標 10
1.4 本文大鋼 11
第二章 、理論探討 13
2.1 模態凝縮法 14
2.2 [M][C][K]重建法 16
2.3 虛擬模態振形法 19
2.3.1 子結構虛擬矩陣[MP][CP][KP]之意義 21
2.3.2 虛擬模態振形法之可行性 22
2.3.3 虛擬模態振形法產生之模態向量正確性 22
2.3.4 虛擬模態振形法之誤差來源 23
2.4 推導多接點轉子結構之虛擬模態向量 25
2.4.1 求解轉子結構之變形模態 25
2.4.2 求解轉子結構之剛體模態 29
2.4.3 兩接點之轉子結構 31
2.5 推導多接點基座結構之虛擬模態向量 36
2.5.1 求解基座結構之變形模態 37
2.5.2 求解基座結構之剛體模態 41
2.5.2.1 範例4-1 42
2.5.2.2 範例4-2 43
2.5.2.3 範例4-3 45
2.5.2.4 範例4-4 47
第三章 、多接點轉子結構建模分析 49
3.1 範例3-1 50
3.2 範例3-2 54
3.3 範例3-3 57
3.4 模態測試 60
第四章 、基座結構建模之實驗驗證 102
4.1 變形模態 104
4.2 剛體模態 106
4.2.1 範例4-1 106
4.2.2 範例4-2 107
4.2.3 範例4-3 109
4.2.4 範例4-4 110
第五章 、結果與討論 152
第六章 、結論 156
參考文獻 158
附錄A-Pseudo mode shape method程式使用說明書 165
附錄B - Curve.m 使用方法 182
簡 歷 187



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