對稱性函數漸變材料的樑之振動分析

在本文中，考慮材料特性會隨著函數變化的對稱性簡支樑，探討其在不同材料特性與不同剪力函數的無因次頻率變化。利用漢米爾頓原理(Hamilton’s principle)推導統御方程式與邊界條件。將運動方程式分離變數法後使用 Galerkin的方法整理，再用四階 Runge-Kutta 的方法來描述振幅與時間的關係。結果顯示在P-FGM下n值增加其無因次頻率變大，S-FGM中p值增加其無因次頻率變小。

關鍵字

無因次頻率；簡支樑；對稱性；函數變化

並列摘要

In this study, we consider the symmetric functionally graded material (FGM) for simply supported beam, which properties are changed functionally. The non-dimensional circular frequency with different properties and different shear function is determined. Hamilton’s principle is used to derive government equation, and boundary conditions. Separate the variables of displacement into position and time by using the method of separation. Then we simplify motion equation to an ordinary differential equation by using Galerkin’s method. The relationship between amplitude and time would be determined by using the 4th order Runge-Kutta method, The result reveal that n of P-FGM increases and the non-dimensional circular frequency also increases, p of S-FGM increases and the non-dimensional circular frequency decreases.

並列關鍵字

simply supported ； the non-dimensional circular frequency ； functionally graded beam ； amplitude

參考文獻

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[2] M. Aydogdu, V. Taskin, Free vibration analysis of functionally graded beams with simply supported edges, Volume 28,pp.1651–6,2007.

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[5] X.-F. Li, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. J Sound Vib 2008.

[6] E. Efraim, M. Eisenberger, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates. J Sound Vib, Volume 299,pp.720–38,2007

國際替代計量

對稱性函數漸變材料的樑之振動分析

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