臺灣博碩士論文加值系統

本文主要探討的部分為以薄板理論研究任意變化厚度之等向性圓盤的應力分布及臨界轉速。以不同之內外徑比及厚度比評估臨界轉速，結果顯示較大的內外徑比或厚度參數均能有效地增加在較低模態下的臨界轉速。
將遺傳演算法 (G.A. ) 與轉移矩陣法結合來分析要達到應力均勻分布和能提升旋轉圓盤之臨界轉速的形狀設計，數值分析結果得出應力均勻分布之例子顯示內外徑比下降則厚度分布變化劇烈。在高轉速的圓盤之厚度分布會比低轉速的分布較陡峭，高轉速的內徑之厚度會較低轉速的高。

In this study, the stress distribution and critical speed of rotating isotropic disk with arbitrary thickness are investigated based on the thin plate theory. The critical speed is evaluated for different values of radius ratio and thickness ratio. The results show that increasing the values of ratio of radii and thickness parameter can effectively increase the critical speed of the plate for a lower order mode.
By incorporating Genetic algorithm (G.A ) method and transfer matrix
analysis, the shape design of rotating disks for uniform stress distribution
and enhancing critical speed has also been implemended. Numerical
results show that for the case of uniform stress, the thickness distribution of
the disk shows larger variation as the radius ratio is decreased.
The thickness distribution of the disk with a higher rotating speed is more precipitous than those at lower rotating speed. The thickness of inner edge for the disk at high rotating speed is thicker than those at low rotating speed.

CONTENTS
Chinese abstract..................................................I
English abstract.................................................II
Acknowledgements................................................III
Contents.........................................................IV
List of tables....................................................V
List of figures.................................................VII
Nomencalture.....................................................XI
CHAPTER 1 INTRODUCTION............................................1
CHAPTER 2 THEORETICAL ANALYSIS....................................4
2.1 Stress analysis...............................................4
2.2 Transfer matrix..............................................11
CHAPTER 3 GENETIC ALOGRITHM......................................14
CHAPTER 4 RESULTS AND DISCUSSION.................................18
4.1 Experiment of circular plate for natural frequency...........19
4.2 Shape design of disks for uniform stress.....................20
4.3 Optimum Young’s modules distribution........................23
4.4 Shape design of disks for critical speed.....................25
CHAPTER 5 CONCLUSIONS............................................26
REFERENCES.......................................................29

LIST OF TABLES

Table 1 Comparison of natural frequencies of a circular plate with Experiment and simulation..............................................................33
Table 2 Geometric dimensions and material properties of a rotating disk for uniform stress..............................................................33
Table 3 GA parameters in searching thickness distribution of rotating disks
for uniform stress...................................................34
Table 4 Thickness distribution of rotating disks of radius ratio 0.2 for uniform stress for different rotating speed.................................35
Table 5 Thickness distribution of rotating disks for uniform stress for different radii ratio at rotating speed 10000RPM............................36
Table 6 Comparisons of thickness distribution of rotating disks for uniform stress in different GA parameters. ( radii ratio= 0.2, 12000RPM)............37
Table 7 GA parameters in searching optimum Young’s modules distribution of rotating disk...............................................................38
Table 8 Optimum Young’s modules distribution of a disk for different radius ratio at rotating speed 12000 RPM (Unit :m )................................39
Table 9 Optimum Young’s modules distribution of a disk of radius ratio = 0.2 for different rotating speed (Unit :m ).....................................40
Table 10 Material properties and GA parameter in searching optimum thickness distribution for maximum critical speed. Radius ratio =0.33, 0.67, and 0.8.........................................................................41
Table 11 Optimum thickness distribution of rotating disks for different radius ratio in increasing critical speed (Unit: m)................................42


LIST OF FIGURES
Figure 2.1 A variable thickness annular plate................................4
Figure 3.1 The relation of encoding and decoding............................42
Figure 3.2 The element coding...............................................42
Figure 3.3 The arrangement of chromosome number.............................42
Figure 3.4 (a) Double point crossover process...............................43
Figure 3.4 (b) Uniform crossover process....................................43
Figure 3.5 Mutation process.................................................44
Figure 3.6 GA evolution process.............................................45
Figure 4.1 (a) Experiment devices...........................................46
Figure 4.1 (b) Experiment devices...........................................47
Figure 4.2 Dimensions of disk specimen......................................47
Figure 4.3 (a) Impulse chart................................................48
Figure 4.3 (b) Response chart...............................................48
Figure 4.4 Frequency response function......................................49
Figure 4.5 Thickness distribution of a disk of radius ratio 0.2 for different rotating speed for uniform stress...........................................51
Figure 4.6 Radial stress distribution of a disk of radius ratio 0.2 for different rotating speed for uniform stress.................................53
Figure 4.7 Circumferential stress distribution of a disk of radius ratio 0.2 for different rotating speed for uniform stress.............................55
Figure 4.8 The relation between fitness and GA iteration of rotating disks with radii ratio 0.2 for uniform stress..........................................57
Figure 4.9 Thickness distribution of rotating disks with rotating speed 10000RPM for uniform stress (a)radii ratio =0.2, (b) 0.4, (c) 0.6.........................................................................58
Figure 4.10 Radial stress distribution of rotating disks with rotating speed 10000RPM for uniform stress (a)radii ratio =0.2, (b) 0.4, (c) 0.6.........................................................................60
Figure 4.11 Circumferential stress distribution of rotating disks with rotating speed 10000RPM for uniform stress (a)radii ratio =0.2, (b) 0.4, (c) 0.6.........................................................................62
Figure 4.12 The relation between fitness and GA iteration of rotating disks with rotating speed 10000 RPM for uniform stress............................64
Figure 4.13 Young's Modules distribution of rotating disks with rotating speed 12000RPM. (a)radii ratio =0.2, (b) 0.4, (c)0.6........................65
Figure 4.14 Radial stress distribution of rotating disks with rotating speed 12000RPM. (a)radii ratio =0.2, (b) 0.4, (c) 0.6............................67
Figure 4.15 Circumferential stress distribution of rotating disks with rotating speed 12000RPM. (a)radii ratio =0.2, (b) 0.4, (c) 0.6......................69
Figure 4.16 The relation between fitness and GA iteration of rotating disks with rotating speed 10000RPM................................................71
Figure 4.17 Young’s modules distribution of rotating disks with radii ratio 0.2. (a) 12000RPM, (b) 10000RPM, (c) 8000RPM................................72
Figure 4.18 Radial stress distribution of rotating disks with radii ratio 0.2. (a) 12000RPM, (b) 10000RPM, (c) 8000RPM.....................................74
Figure 4.19 Circumferential stress distribution of rotating disks with radii ratio 0.2. (a) 12000RPM, (b) 10000RPM, (c) 8000RPM..........................76
Figure 4.20 The relation between fitness and GA iteration of rotating disks with radii ratio 0.2........................................................78
Figure 4.21 Thickness distribution of rotating disks for critical speed
(a) =0.33, (b) =0.67, (c) =0.8...........................................79
Figure 4.22 Radial stress distribution of rotating disks for critical speed
(a) =0.33, (b) =0.67, (c) =0.8...........................................81
Figure 4.23 Circumferential stress distribution of rotating disk for critical speed (a) =0.33, (b) =0.67, (c) =0.8.....................................83
Figure 4.24 The relation between fitness and GA iteration of rotating disks for critical speed..............................................................85
Figure 4.25 Thickness distribution of rotating disks with different GA
Parameters for uniform stress.....................................86

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