Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory

2011 ◽  
Vol 94 (1) ◽  
pp. 221-228 ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
S. Sahmani
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Strain Gradient ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Functionally Graded ◽  
Timoshenko Beam Theory ◽  
Size Dependent

Free Vibration Analysis of Shafts on Resilient Bearings Using Timoshenko Beam Theory

1999 ◽  
Vol 121 (2) ◽  
pp. 256-258 ◽  
Author(s):  
S. Karunendiran ◽  
J. W. Zu
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Frequency Equation ◽  
Timoshenko Beam Theory ◽  
Mode Shapes ◽  
Complex Eigenvalues ◽  
First Time

This paper presents an analytical method adopted for the free vibration analysis of a shaft, both ends of which are supported by resilient bearings. The shaft is modeled by Timoshenko beam theory. Based on this model exact frequency equation to calculate complex eigenvalues is derived and presented in complex compact form for the first time. Explicit expressions to compute the corresponding mode shapes are also presented.

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