彈性撓度變化對於空間彎樑自然振動頻率之影響

Influence of elastic flexibility on the frequencies of natural vibration of spatially curved beams

吳孟達(Meng-Da Wu)

指導教授 ： 史耀東 ； 魏哲弘

大同大學/工程學院/機械工程學系所/碩士(2006年)

摘要

本篇論文討論空間樑之結構，樑之截面積在不同曲率及扭率的情下，求取自然頻率的相關變化。沿著樑的中心線上的每一個點都有三個方向移動位移及所在的截面都有三個轉動角度。特徵值問題求自然頻率之各種不同樑截面積比、直徑與長度比、E/G 比及各種不同邊界條件。藉以Runge-Kutta積分法，產生不同方程式以adjoint operator system 去運算，最後在以不同邊界條件，代入方程式，用fortran寫程式，以七個控制變因，算出數據，用Tecplot畫出相關圖，並詳加以討論。

關鍵字

自然振動頻率 ； 空間彎樑

並列摘要

This thesis discusses the structure of the spatially beam as the difference conditions between curvature and torsion in the cross-section of the beam
ask the change relation of the natural vibration. Every point which follows the centerline of the beam has three translation displacements and three rotational angles of the cross-section area. The Eigenvalue problem is solved the natural frequencies of varying pre-twisted angles of the rectangular cross-section area, slenderness ratio, E/G ratio, all kinds of end conditions. Using the method of Runge-Kutta integration gets the difference equations. Then, adjoint operator system operates them. Finally, the equations of the difference end conditions write the fortran program by controlling seven factors. The datum of the program draw the charts by using Tecplot. The datum discuss the relational change.

並列關鍵字

the frequencies of natural vibration ； spatially curved beams

參考文獻

[1] B. Tabarrok, A.M. Sinclair, M. Farshad, H. Yi, On the dynamics of spatially curved and twisted rods-a finite element formulation, Journal of Sound and Vibration 123 (1988) 315-326.

[2] B. Tabarrok, M. Farshad, H. Yi, Finite element formulation of spatially curved and twisted rods, Computer Methods in Applied Mechanics and Engineering 70 (1988) 275-299.

[3] R. Davis, R.D. Henshell, G.B. Warburton, Constant curvature beam finite elements for in-plane vibration, Journal of Sound and Vibration 25 (1972) 561-576.

[4] T.M. Wang, A.J. Laskey, M.F. Ahmad, Natural frequencies for out-of-plane vibrations of continuous curved beams considering shear and rotary inertia, International Journal of Solids and Structures 20 (1984) 257-265.

[5] W.L. Cleghorn, B. Tabarrok, T.W. Lee, vibration of rings with unsymmetrical cross-section: a finite element approach, Journal of Sound and Vibration 168 (1993) 93-113.