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

碩士 === 中原大學 === 機械工程研究所 === 105 === 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 prin...

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Main Authors:	Cheng-Yen Chen-Wu, 陳吳政彥
Other Authors:	Yan-Shin Shih
Format:	Others
Language:	en_US
Published:	2017
Online Access:	http://ndltd.ncl.edu.tw/handle/97754119008983718465

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spelling	ndltd-TW-105CYCU54890602017-09-22T04:33:53Z http://ndltd.ncl.edu.tw/handle/97754119008983718465 Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function 軸向指數函數級化Timoshenko樑之振動分析 Cheng-Yen Chen-Wu 陳吳政彥碩士中原大學機械工程研究所 105 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 Yan-Shin Shih 施延欣 2017 學位論文 ; thesis 93 en_US
collection	NDLTD
language	en_US
format	Others
sources	NDLTD
description	碩士 === 中原大學 === 機械工程研究所 === 105 === 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
author2	Yan-Shin Shih
author_facet	Yan-Shin Shih Cheng-Yen Chen-Wu 陳吳政彥
author	Cheng-Yen Chen-Wu 陳吳政彥
spellingShingle	Cheng-Yen Chen-Wu 陳吳政彥 Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function
author_sort	Cheng-Yen Chen-Wu
title	Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function
title_short	Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function
title_full	Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function
title_fullStr	Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function
title_full_unstemmed	Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function
title_sort	vibration analysis of timoshenko beam of the axially and functionally graded material with exponent function
publishDate	2017
url	http://ndltd.ncl.edu.tw/handle/97754119008983718465
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Vibration Analysis of Timoshenko Beam of the Axially and Functionally Graded Material with Exponent Function

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