Analytical Solutions for The Torsional Vibrations of Variable Cross-Section Rods

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International Journal of Engineering and Applied Sciences
Volume:2 Issue:4
Analytical Solutions for The Torsional Vibrations of Variable Cross-Section Rods

Analytical Solutions for The Torsional Vibrations of Variable Cross-Section Rods

Authors : M RAFİEE, S Jafari MEHRABADİ, N RASEKHSALEH

Pages : 64-71

View : 33 | Download : 7

Publication Date : 2010-12-01

Article Type : Research Paper

Abstract :The objective of this paper is to present exact analytical solutions for the torsional vibration of rods with nonuniform cross-section. Using appropriate transformations the equation of motion of torsional vibration of a rod with varying cross-section is reduced to analytically solvable standard differential equations whose form depends upon the specific area variation. Solutions are obtained for a rod with for a polynomial area variation. The solutions are obtained in terms of special functions such as Bessel and Neumann functions. Simple formulas to predict the natural frequencies of non-uniform rods with various end conditions are presented. The natural frequencies of variable cross-section rods for these end conditions are calculated and their dependence on taper is discussed
Keywords : Torsional Vibration, Isotropic, Rod, Variable Cross Section, Analytical Solution

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