臺灣博碩士論文加值系統

空間彎樑振動的統御方程式是由運動平衡及應變與位移之關係求得，此無因次系統的微分方程式是由空間彎樑三個位移與三個轉動角所求得。假設位移函數的時間部分為簡諧型態，可將為分方程式化簡為僅樑與樑座標相關的常微分方程。為了觀察位移及撓角的關聯，將十二條方程式化減為六條位移及撓角的微分方程式並考慮邊界條件的限制，當T<<1及T>>K時，以擾動法探討此一特徵值問題的振動頻率。並在不同的材料性質與外型下，討論扭矩對於頻率的影響。

For spatially curve beam, a set of governing equations consisting of equilibrium motion equations and strain-displacement and constitutive relations. This system of non-dimensional ordinary differential equations is obtained in three translation displacements and three rotational angles of the beam. The time dependency in the displacement functions is assumed in exponential form. The twelve governing equations are simplified to a time-independence formulation. In order to observe the relations of displacement vector and rotation vector, simplified to six ordinary differential equations and considering the restriction of boundary condition. The frequency of vibration of eigenvalue problem is solved by using perturbation method when T<<1 and T>>K. At the same time, to discuss the effects of the torsion of the frequency when the different material quality and geometrically form.

LIST OF CONTENTS

ACKNOWLEDGMENT………………………………………...…..…...…I
CHINESE ABSTRACT……………………………………………….……II
ENGLISH ABSTRACT……………………………………………...….…III
LIST OF CONTENTS……………………………………..…………...….IV
LIST OF FIGURES………………………………………………….…….VI
NOMENCLATURE………………………………………….…………..VIII

CHAPTER I
INTRODUCTION…………………………………………………………...1
1.1 Research Motive………………………………….…………….1
1.2 About Perturbation Method………………………….…………5

CHAPTER II
MATHEMATICAL FORMULATION..……………………………………..8
2.1 Basic Assumption………………………………………………8
2.2 Local Coordinate System……………………………….………9
2.3 Motion Equations……………………………………..……….12
CHAPTER III
PERTURBATION METHOD…………..…….............................................15
3.1 Non-dimensional Parameters…………………………….……15
3.2 Perturbation Method…………………………….…………….18

CHAPTER IV
RESULTS AND DISCUSSIONS…………………………..……...……….22
4.1 Solve The Lowest Natural Frequencies…………………….…22
4.2 Numerical Analysis……………………………………...…….38


CHAPTER V
CONCLUSIONS…………………...........…………………………………44
REFERENCE….……………………………………………………...……45
45

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