Free vibration of functionally graded graphene platelet-reinforced porous beams with spinning movement via differential transformation method

2021 ◽  
Author(s):  
Hang Xu ◽  
Yan Qing Wang ◽  
Yufei Zhang
Keyword(s):  
Free Vibration ◽  
Transformation Method ◽  
Functionally Graded ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Graphene Platelet

Free Vibration Analysis of Rotating Tapered Bresse-Rayleigh Beams Using the Differential Transformation Method

2009 ◽  
Author(s):  
Dominic R. Jackson ◽  
S. Olutunde Oyadiji
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Free Vibration Analysis ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Algebraic Equations ◽  
Differential Transformation ◽  
Rayleigh Beam

The free vibration characteristics of a rotating tapered Rayleigh beam is analysed in this study. First, the strain-displacement relationship for the rotating beam is formulated and used to derive the kinetic and strain energies in explicit analytical form. Second, Hamilton’s variational principle is used to derive the governing differential equation of motion and the associated boundary conditions. Third, the Differential Transformation Method (DTM) is applied to reduce the governing differential equations of motion and the boundary conditions to a set of algebraic equations from which the frequency equation is derived. Next, a numerical algorithm implemented in the software package Mathematica is used to compute the natural frequencies of vibration for a few paired combinations of clamped, pinned and free end conditions of the beam. Also, the variation of the natural frequencies of vibration with respect to variations in the rotational speed, hub radius, taper ratio and the slenderness ratio is studied. The results obtained from the Bresse-Rayleigh theory are compared with results obtained from the Bernoulli-Euler and Timoshenko theories to demonstrate the accuracy and relevance of their application.

Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams

2015 ◽  
Vol 29 (3) ◽  
pp. 1207-1215 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Majid Ghadiri ◽  
Erfan Salari ◽  
Seied Amir Hosein Hoseini ◽  
Gholam Reza Shaghaghi
Keyword(s):  
Vibration Analysis ◽  
Transformation Method ◽  
Functionally Graded ◽  
Differential Transformation Method ◽  
Differential Transformation

Differential Transformation Method for Temperature Distribution in a Radiating Fin

2011 ◽  
Vol 42 (5) ◽  
pp. 403-414 ◽  
Author(s):  
M. Rahimi ◽  
M. J. Hosseini ◽  
Amin Barari ◽  
Ganji Domairry
Keyword(s):  
Temperature Distribution ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Differential Transformation

Differential transformation method for circular membrane vibrations

2020 ◽  
Vol 61(12) (2) ◽  
pp. 333-350
Author(s):  
Jaipong Kasemsuwan ◽  
◽  
Sorin Vasile Sabau ◽  
Uraiwan Somboon ◽  
◽  
...  
Keyword(s):  
Transformation Method ◽  
Differential Transformation Method ◽  
Circular Membrane ◽  
Differential Transformation ◽  
Membrane Vibrations
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