Free vibration analysis of micro rotating beams based on the strain gradient theory using the differential transform method: Timoshenko versus Euler-Bernoulli beam models

2017 ◽  
Vol 65 ◽  
pp. 336-348 ◽  
Author(s):  
Hadi Arvin
Keyword(s):  
Free Vibration ◽  
Strain Gradient ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Bernoulli Beam ◽  
Transform Method ◽  
Differential Transform ◽  
Euler Bernoulli Beam

Free Vibration Analysis of Rotating Euler–Bernoulli Beam with Exponentially Varying Cross-Section by Differential Transform Method

2018 ◽  
Vol 18 (02) ◽  
pp. 1850024 ◽  
Author(s):  
Mostafa Nourifar ◽  
Ali Keyhani ◽  
Ahmad Aftabi Sani
Keyword(s):  
Free Vibration ◽  
Recurrence Relation ◽  
Cross Section ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Differential Transform Method ◽  
Bernoulli Beam ◽  
Transform Method ◽  
Differential Transform ◽  
Euler Bernoulli Beam

In this paper, the free vibration analysis of non-uniform rotating Euler–Bernoulli beam is carried out. It is assumed that the beam has exponentially decaying circular cross-section. In order to solve the problem, the differential transform method (DTM) is utilized. Based on our knowledge, we claim that the recurrence relation presented herein is an elaborate recurrence relation which has been obtained for ordinary differential equations. Non-dimensional natural frequencies of the beam are obtained and tabulated for different values of the beam parameters such as taper ratio and rotating speed. Furthermore, the finite element method (FEM) is employed to solve the problem. Comparison of the results obtained by DTM and FEM indicates the accuracy of proposed solutions.

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