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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 66
Edited by: B.H.V. Topping
Paper VI.2

A Computational Method for Free Transverse-Vibration Analysis of Stepped-Beams

K. Abhary+ and A. Nourbakhsh#

+School of Advanced Manufacturing and Mechanical Engineering, University of South Australia, Mamson Lakes Campus, SA, Australia
#Department of Mechanical Engineering, Tehran University, Tehran, Iran

Full Bibliographic Reference for this paper
K. Abhary, A. Nourbakhsh, "A Computational Method for Free Transverse-Vibration Analysis of Stepped-Beams", in B.H.V. Topping, (Editor), "Computational Mechanics: Techniques and Developments", Civil-Comp Press, Edinburgh, UK, pp 129-133, 2000. doi:10.4203/ccp.66.6.2
In this method a stepped beam is substructured into its n spans, each of which, except the ones at extreme ends, is treated as a uniform continuous beam clamped to its adjacent spans. This implies that at each step of the shaft any two adjacent spans have identical displacements, slopes, bending moments and shearing forces. Theoretically speaking, these boundary conditions along with those of the extreme ends (total of 4n), when applied to the vibration equation of corresponding spans, generate a set of 4n equations. Then, this set of simultaneous equations should be solved to generate natural frequencies of the beam as well as the constants of the vibration equation of all spans. An efficient mathematical algorithm is furnished herein to cluster the above-mentioned equations into groups of four and solve them one after the other. 'The algorithm is programmed in VISUAL C++, and its accuracy justified via a number of examples.

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