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系統識別號 U0026-2507201915512500
論文名稱(中文) 虛擬模態振型法於構件模態綜合法之應用
論文名稱(英文) Application of the Method of Pseudo Mode Shape in Component Mode Synthesis
校院名稱 成功大學
系所名稱(中) 航空太空工程學系
系所名稱(英) Department of Aeronautics & Astronautics
學年度 107
學期 2
出版年 108
研究生(中文) 湯育澄
研究生(英文) Yu-Cheng Tang
學號 P46061178
學位類別 碩士
語文別 中文
論文頁數 74頁
口試委員 指導教授-江達雲
口試委員-楊世銘
口試委員-崔兆棠
口試委員-林章生
中文關鍵字 構件模態綜合法  模型縮減  虛擬模態振型 
英文關鍵字 component modal synthesis  model reduction  pseudo mode shape 
學科別分類
中文摘要 在大型複雜結構進行分析時,一般可藉由構件模態綜合法將結構依功能性分割成數個構件,進一步對各個構件進行有限元素建模或模態測試分析,再將相鄰構件綜合成近似整體結構的縮減模型。但在上述綜合的過程中,即可能會面臨有限元素模型與模態測試所得之頻響函數二種不同型態資訊之結合問題,導致難以得到整體結構模型之動態特性。
本文探討如何應用虛擬模態振型方法於構件模態綜合法,當僅能量測構件限定自由度上的輸入與輸出信號以及對應之頻率響應函數,透過此法的虛擬模態振型矩陣將構件的頻率響應函數轉換得到構件在物理座標的替代模型矩陣,再將此構件的替代模型與相鄰有限元素模型綜合並能適當地描述整體模型之動態特性。
本文研究重點為如何運用虛擬模態振型來提升模態綜合分析的精準性。吾人也針對前人發表的虛擬模態振型法進行改良,引入全虛擬模態振型矩陣回推等效的替代模型,可以省去在限定自由度之振型資訊的計算程序,轉換得到的替代模型結構依然保有原複雜構件的動態特性。由數值模擬顯示,虛擬模態振型法可有效彌補模態振型資訊不足的問題,提升此法於構件模態綜合法分析時的有效性。
英文摘要 Conventional finite-element analysis may encounter the problem of insufficient computational resources especially when the structure system under consideration is large and complex. In order to reduce the model order of a system, Component Mode Synthesis is one of the reduction methods, which can make the structure system be divided into several components according to the features. Further finite element modeling or modal test analysis is performed on each component, and then these components are integrated into an approximate overall structural model. However, in the above synthesize process, it may face the combination of the two different types of information between the finite element model and the frequency response function obtained by the modal test, which makes it difficult to obtain the dynamic characteristics of the overall structural model.
This thesis discusses how to apply the pseudo mode shape method to the component modal synthesis method. When the corresponding frequency response function of the component in the defined degree of freedom is measured, the pseudo mode shape matrix of the method converts the frequency response function of the component to obtain the substitute model matrix of the component at the physical coordinate. The surrogate model of this component is integrated with the finite element model into an approximate overall model, and the dynamic characteristics of the overall model can be appropriately described.
The focus of this thesis is on how to use pseudo mode shapes to improve the accuracy of modal synthesis analysis. We improved the pseudo mode shape method proposed in the past, and used the full pseudo mode matrix to derive the equivalent analysis model, which can save the calculation programs of the vibration mode information at the joint. The equivalent analysis model still maintain the important dynamic characteristics of the original system. In this paper, a two-dimensional beam is taken as an example to verify the feasibility of the method.
論文目次 摘要 I
致謝 IX
目錄 X
圖目錄 XIII
表目錄 XIV
第一章 緒論 1
1.1 引言 1
1.2 模態分析與動態分析 3
1.3 文獻回顧 4
1.4研究動機與目的 7
1.5 論文架構 8
第二章 構件模態綜合法 9
2.1 引言 9
2.2 模型縮減 11
2.2.1 Guyan縮減法 13
2.2.2 模態縮減法(Modal Reduction Method) 15
2.3 構件模態綜合法 16
第三章 虛擬模態振型法 22
3.1 引言 22
3.2 模態分析理論 23
3.3 引入虛擬模態振型法於構件模態綜合法 25
3.4 虛擬模態振型法 26
3.4.1 模態質量正規化 27
3.4.2 模態參數特性 30
3.5 虛擬模態振型矩陣 32
3.5.1 相似矩陣 34
3.6 全虛擬模態振型矩陣 37
第四章 數值模擬 39
4.1 引言 39
4.2 樑模型之模擬分析 39
4.2.1 構件模態綜合法之模擬分析 41
4.2.2 虛擬模態振型法之模擬分析 42
第五章 結論 47
參考文獻 49
符號命名 52
圖目錄 54
表目錄 60

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蔡篤慶, 應用構件模態綜合法於結構動態分析之研究, 碩士論文,國立成功大學航空太空工程研究所,2010.
王英洺, 大型結構之力耦合分析與驗證, 碩士論文,國立成功大學航空太空工程研究所,2010.
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