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

Year 2010, Volume: 2 Issue: 4, 64 - 71, 01.12.2010

M. Rafiee S. Jafari Mehrabadi N. Rasekh-saleh

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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