轉軸系統在生活中相當常見，空氣動力引擎與發電機都是轉軸系統的實際例子。由於目前轉軸系統的趨勢都朝向高效率與高功率輸出，該種系統的動態特性顯得越來越重要。不良的動態特性的設計會導致大震動響應、低能量效率、使用者不良的體驗、甚至是系統的損壞故障。基於這些原因，系統的動態特性需要被仔細的設計與考慮，或是被修正。然而有些系統在實際上會因為太過於複雜而難以被準確的模擬，因此基於位移響應的逆結構修改方法是一個很有潛力的解決方案。
本論文提出一基於位移響應的逆結構修改方法以提升轉軸系統的動態表現。跟其他在結構修改領域的方法，該方法有許多的優點，包含: (a)分析程序較為直觀與直接，可根據理想的動態特性去推算出需要修改的建議、(b)分析過程不需要系統之元素矩陣(質量、阻尼與剛性矩陣)或是模態資料、(c)繁瑣的反覆試驗可以被避免、(d)透過實驗獲得的數據可以直接被使用、(e)可設計與修正多種動態特性。因為這些許多的優點，該方法在提出後持續獲得了許多的關注與研究。相關的文獻都包含在本論文中，同時在該領域當前的挑戰(理論上與實際應用上)也被整理出來，本論文將某些挑戰作為出發點，並嘗試解決那些問題。
首先，一基於位移響應方法將被延伸，動態特性的設計的問題將以最佳化的方法解決，研究結果可應用在設計多種的動態特性且有能力同時包含多種類型且多點的結構修改形式。該方法的實用性由模擬以及實驗驗證，實驗為在一齒輪轉子軸承系統上單純使用實驗數據以指定自然頻率與反共振頻率。此外，也透過實驗驗證，可以單依賴實驗數據去提供最佳的結構修改位置以達到最高的第一彎曲自然頻率。
如何準確地量測轉動方向或扭轉方向的位移響應為在實際應用基於位移響應的逆結構修改方法中的一個棘手問題。本論文提出一基於位移響應的間接量測技術，該技術將使用T型塊作為量測上的輔助且不需要被量測系統的理論模型。該技術可容納不同數量與不同位置的輸入源與輸出源，且相較於文獻中提出的方法有較優的結果。該技術現在可應用在許多領域上，如模態分析、模型更新、與結構修正。
此外，本論文也研究透過多次系統耦合的自然頻率設計方法。本論文考慮的次系統為轉軸系統，而轉軸系統有些會相當複雜。研究的方法為使用位移響應耦合法與結合最佳化演算法，本論文提出的方法只需要每個次系統在耦合位置處的位移響應資訊，可透過一多自由度、可修改的接頭去設計整體系統的彎曲自然頻率與扭轉自然頻率(可同時或獨立設計)。本論文用許多的模擬去驗證該方法，而實際上，該方法可整合本論文中提出的位移響應量測法，達到動態特性優化的結果。

The applications of rotor systems are common in our daily life and industry. Aero engines and power generating equipment are good examples of rotor systems. Due to the recent increasing interest in higher energy efficiency and higher power density, the structural dynamic performance of such a rotor system is becoming more important. A poor structural dynamic design can cause large vibration responses, low power efficiencies, bad user experiences, or possibly a complete failure of the system. For these reasons, the dynamic properties need to be thoroughly considered, designed, and sometimes modified. However, there are cases in which the system of interest is too complex to be accurately modelled, thus making accurate simulations difficult or infeasible. For this problem, the receptance-based inverse structural modification method can potentially be a good solution.
In this thesis, a receptance-based inverse structural modification method is studied to improve a rotor system’s dynamic performance. Such a method has a number of merits compared to other methods in the area of structural modification, which include (a) the procedure of the analysis is straightforward in the sense that the modifications to be made are determined by the desired dynamical properties, (b) it does not require the system matrices (M, C, and K) or the modal data to carry out the analysis, (c) the tedious trial-and-error approach can be avoided, (d) experimental data can be directly used in the method, and (e) various dynamic properties can be assigned. As a result, the method continually receives research interest although the idea was proposed slightly more than a decade ago. The relevant work in this area of research is reviewed and the challenges are identified regarding its theoretical developments and practical applications. Some of the challenges are taken as the objectives of this study.
First, the receptance-based method is further extended and the assignment problem is cast as an optimization problem to assign various dynamical properties using more than one form of modifications and accommodate structural modifications at more than one location. Several forms of modifications previously reported in the literature can be simultaneously included in the extended method. The applicability of the method is demonstrated by a number of simulations and experiments. It is applied to a laboratory geared rotor-bearing system to achieve natural frequency and antiresonant frequency assignments solely using experimental receptances. Additionally, it is shown by experiments that the locations of the given modifications can be determined without a numerical model so that the highest first bending natural frequency of a rotor system can be achieved.
A big unsolved challenge in implementing the receptance-based structural modification method in practice is the lack of high-quality measurement of rotational (in bending) or torsional receptances. A receptance-based indirect measurement technique using a T-block attachment is proposed to address this issue. The numerical model of the system of concern is not required. The proposed technique can take account of the information from a number of excitations and responses, and provides the flexibility in their choices of location. The proposed technique has shown better performance over the torsional receptance estimation technique in the literature and is extended to estimate high-quality rotational receptances. The estimated receptances can now be used in various applications such as modal analysis, model updating, and structural modification.
Moreover, the frequency assignment via coupling of subsystems is studied. The subsystems considered are rotor systems which can be rather complex. The theory is developed based on Receptance Coupling technique and formulated as an optimization problem, and only the receptances at the connection ends of the subsystems of interest are required. Both bending natural frequencies and torsional natural frequencies can be assigned using a modifiable joint with multiple DoFs, respectively or simultaneously. The technique is demonstrated by a few simulations and is possible to be implemented in practice through the proposed rotational/torsional receptance estimation technique.

摘要 i
Abstract iii
Acknowledgements v
Content vi
List of figures ix
List of tables xiii
Nomenclature xv
1. Introduction 1
1.1. Background 1
1.2. Motivation 4
1.3. The scope of this research 5
1.4. Original contributions 8
2. Literature review 10
2.1. Forward structural modification 10
2.2. Inverse structural modification 13
2.2.1. Receptance method 15
2.3. Rotational FRF measurement 21
2.4. Open problems 26
3. Finite Element modelling for rotordynamic analysis 32
3.1. FE models 32
3.1.1. Coordinate system 34
3.1.2. Equations of motion 36
3.2. Modelling of common components 39
3.3. Eigenvalue problem 46
3.4. A case study 49
4. Receptance-based inverse structural modification methods 58
4.1. Receptance and dynamic stiffness matrix 58
4.2. Receptance method for passive control 60
4.2.1. Rank-one modification 60
4.2.2. Spring-mass oscillator 68
4.3. Receptance method for active control 74
4.3.1. Partial pole assignment 83
5. Inverse structural modifications of a geared rotor-bearing system 89
5.1. Theoretical development 90
5.2. Experimental setup 94
5.3. Numerical simulation 96
5.4. Experimental results 109
5.4.1. Natural frequency assignment 110
5.4.2. Antiresonant frequency assignment 114
5.4.3. Determination of the highest first bending natural frequency 117
5.5. Conclusions 120
6. Identification of Torsional Receptance 122
6.1. Theoretical development 122
6.2. Numerical simulation 128
6.2.1. Theoretical model 128
6.2.2. Model updating of the T-block 142
6.3. Experimental validation 144
6.3.1. Torsional receptance estimation 145
6.3.2. Modal parameter estimation 147
6.3.3. Repeatability of the estimated receptances 149
6.3.4. Synthesis of frequency response functions 151
6.3.5. Different selections of the response 152
6.4. Application 154
6.5. Conclusions 163
7. Frequency Assignment by Coupling of Subsystems 165
7.1. Receptance coupling technique 165
7.1.1. Classical receptance coupling technique 166
7.1.2. Receptance coupling of three subsystems 168
7.2. Numerical simulation 170
7.2.1. Numerical model 171
7.2.2. Bending frequency assignment 174
7.2.3. Torsional frequency assignment 177
7.2.4. Two-frequency assignment 179
7.3. Estimation of rotational receptances 181
7.4. Conclusion 186
8. Conclusions and Outlook 187
8.1. Conclusions 187
8.2. Outlook 190
Appendix A 191
Appendix B 193
Bibliography 195

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