軸向指數函數級化Timoshenko樑之振動分析

Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function

陳吳政彥(Cheng-Yen Chen-Wu)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2017年)

https://doi.org/10.6840/cycu201700683

摘要

中文摘要
在文中考慮函數級化的Timoshenko beam，探討其在函數級化材料下的自由振動分析。先利用漢米爾頓(Hamilton)原理求得其運動方程式與邊界條件，再以滿足邊界條件的模態函數，利用Galerkin's Method將運動方程式化簡為以時間為變數的方程式，然後利用Runge-Kutta的數值方法求得振幅對時間的關係圖，並以此計算自然頻率 。隨著 的逐漸改變，可換算得到不同的自然頻率 ，之後再與自然頻率 比較。

關鍵字：Timoshenko beam、函數級化材料、自然頻率、自由振動

關鍵字

函數級化材料 ； 自然頻率 ； 自由振動

並列摘要

Abstract
In this study, consider a Timoshenko beam based on the functionally graded material, to analyze the natural frequency with several different materials. First , we derive the equations of motion and boundary conditions by Hamilton's principle, and then use the Galerkin's Method to reduce the equations of motion to ordinary differential equations, then apply Runge-Kutta method to obtain the Relationship of amplitude ratio verse time. Each has a different . Finally compare natural frequency with natural frequency .

Keyword: Timoshenko beam, functionally graded material, natural frequency, free vibration

並列關鍵字

Timoshenko beam ； functionally graded material ； natural frequency ； free vibration

參考文獻

[1] Birman V, Byrd L.W. Modeling and analysis of functionally graded materials and structures. Applied Mech Rev, 60 (2007) 195–216

[2] Tong X, Tabarrok B, Yeh K. Vibration analysis of Timoshenko beams with non-homogeneity and varying cross-section. J Sound Vib, 186 (1995) 821–835

[3] Esmailzadeh E, Ohadi A. Vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads. J Sound Vib, 236 (2000) 443–456

[4] Leung A.Y.T, Zhou W.E, Lim C.W, Yuen R.K.K, Lee U. Dynamic stiffness for piecewise non-uniform Timoshenko column by power series—Part I: conservative axial force Int J Numer Meth Eng, 51 (2001) 505–529

[5] Zhou D, Cheung Y. Vibrations of tapered Timoshenko beams in terms of static Timoshenko beam functions. J Appl Mech, 68 (2001) 596–602