scholarly journals Free vibration analysis of pre-stressed FGM Timoshenko beams under large transverse deflection by a variational method

2016 ◽  
Vol 19 (2) ◽  
pp. 1003-1017 ◽  
Author(s):  
Amlan Paul ◽  
Debabrata Das
Keyword(s):  
Variational Method ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Timoshenko Beams ◽  
Transverse Deflection

FREE VIBRATION ANALYSIS OF NON-UNIFORM TIMOSHENKO BEAMS USING DIFFERENTIAL TRANSFORM

1998 ◽  
Vol 22 (3) ◽  
pp. 231-250 ◽  
Author(s):  
Cha’o Kuang Chen ◽  
Shing Huei Ho
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Present Method ◽  
Series Solution ◽  
Free Vibration Analysis ◽  
Timoshenko Beams ◽  
Differential Transform ◽  
Vibration Problems ◽  
Algebraic Operations

This study introduces using differential transform to solve the free vibration problems of a general elastically end restrained non-uniform Timoshenko beam. First, differential transform is briefly introduced. Second, taking differential transform of a non-uniform Timoshenko beam vibration problem, a set of difference equations is derived. Doing some simple algebraic operations on these equations, we can determine any i-th natural frequency, the closed form series solution of any i-th normalized mode shape. Finally, three examples are given to illustrate the accuracy and efficiency of the present method.

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