臺灣博碩士論文加值系統

本文所探討分為兩部分，一是考慮剪力變形與旋轉慣量之非等向性圓環板的振動與臨界挫曲負荷，包含CF（內徑固定外徑自由）與SS（內徑外徑簡支撐）之不同邊界條件；另一則是探討同心圓支撐，對提升非等向性圓環板臨界挫曲負荷的有效性評估，而此圓環板分別承受平面負荷與扭力。

為求解此穩定性問題，將圓環板的位移函數分別以三角級數及Power Series函數，代入系統之應變能、動能與外力所做的功，再利用雷利-里茲法求得系統之自然頻率與臨界負荷。針對不同邊界條件來探討圓環板厚度、材料剛性比、彈性支撐和同心圓支撐位置的變化，對自然頻率的影響與臨界挫曲負荷之穩定性分析，並以圖表表示之。

Investigation in this research is divided into two parts. One is the consideration on the vibration and buckling load of the orthotropic annular plate taking account of shear deformation and rotary inertia, including CF (clamped at inner edge and free at outer edge) and SS (simply supported at inner edge and outer edge) boundary conditions. The other part is to investigate the effect of concentric ring supports on the effectiveness of the enhancement of the buckling load of the orthotropic annular plate. This annular plate bears the in-plane force and torque separately in the mathematical formulation.

In order to solve this stability problem, the position shift functions of the annular plate shall utilize the trigonometric series and power series function that will be substituted into the work made by the potential energy, kinetic energy and external force. Then the natural frequency and the buckling load of the system are obtained by utilizing the Rayleight-Ritz’s Method. Aiming at different boundary conditions, investigation is conducted on the thickness of the annular plate, orthotropic rigidity ratio, flexibility and the concentric ring supports position change. Analysis is conducted on the effect of the natural frequency and the stability of the buckling load that will be expressed by diagram and chart.

ACKNOWLEDGEMENTS…………………………….………………...........I
ENGLISH ABSTRACT……………..…………………………………….....II
CHINESE ABSTRACT……………………………………………….........IV
TABLE OF CONTENTS………………………….……………….…….......V
LIST OF TABLES……………………………….……………………....VIII
LIST OF FIGURES……………………………………………………….....X
CHAPTER 1 INTRODUCTION…………………………………………........1
1.1 Motivation…………………………….………………….………..1
1.2 Literature Review……………………………….………………..3
1.3 Scope of the Present Study………………………………………6
CHAPTER 2 THEORETICAL ANALYSIS…………………..…….…….......8
2.1 Orthotropic material property………………………………….8
2.2 Energy equation…………………………………………………..11
2.3 Vibration and stability of orthotropic Mindlin plates
under in-plane load………………………………………………14
2.3.1 The orthotropic Mindlin annular plate with CF
boundary condition……………………………….…………14
a. Stress due to in-plane force………………….……...…14
b. Rayleigh-Ritz’s Method…………………….…….……….16
c. Dimensionless form………………………..………………..21
2.3.2 The orthotropic Mindlin annular plate with SS
boundary condition………………………………………….25
a. Stress due to in-plane force………………….………...25
b. Rayleigh-Ritz’s Method……………………….….……….26
c. Dimensionless form……………..……………………….….29
2.4 Vibration and stability of orthotropic thin plates under
in-plane load/torque…………………………………………….30
2.4.1 The orthotropic annular plate with one or two
internal ring supports…………………………………….30
a. Stress due to in-plane force……………..……..………30
b. Rayleigh-Ritz’s Method……………….…….…………….31
c. Dimensionless form……………………….…………..…….36
CHAPTER 3 RESULTS AND DISCUSSION………….……………..…......40
3.1 Study of convergence……………………….……………………41
3.2 Vibration and stability of orthotropic Mindlin plates
under in-plane load………………………………………………43
3.2.1 Effect of the orthotropic Mindlin annular plate for
in-plane load…………………………………….………….43
3.2.2 Effect of the orthotropic Mindlin annular plate for
thickness………………………………………………….….46
3.2.3 Effect of the orthotropic Mindlin annular plate for
flexibility……………………………………………………48
3.2 Vibration and stability of orthotropic thin plates under
in-plane load/torque…………………………………………….51
3.2.1 Effect of the orthotropic annular plate with one
internal ring support for in-plane load………………50
3.2.2 Effect of the orthotropic annular plate with two
internal ring supports for in-plane load…………….54
3.2.3 Effect of the orthotropic annular plate with two
internal ring supports for in-plane torque………….58
CHAPTER 4 CONCLUSIONS……………...……….………………….....106
REFERENCES……………………………………….……..………….....109

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