Title: Three-dimensional vibration analysis of a finite cylinder using the generalised differential quadrature method

Authors: Reza Teymoori Faal; Behnam Ghalamchi

Addresses: Faculty of Engineering, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran ' Faculty of Engineering, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran; Lappeenranta University of Technology, LUT Metal, Laboratory of Machine Design, P.O. Box 20, FIN-53851 Lappeenranta, Finland

Abstract: Using the Navier's equations of the motion in cylindrical coordinate, vibration analysis of a finite cylinder is accomplished. These equations are transformed into the dimensionless forms in terms of non-dimensional displacements and time. The different boundary conditions are considered for this problem which the former analytical and semi-analytical methods could not treat them. Two ends boundary condition namely fixed-fixed and fixed-free are examined. The dimensionless governing equations of the motions in conjunction with the boundary condition are discretised making use of the generalised differential quadrature (GDQ) method. The ensuing system of algebraic equations in terms of displacement components leads to an eigenvalue problem to find the natural frequencies of the problem. The comparison of the results with some earlier works validates the methodology and formulation of the problem.

Keywords: Navier equations; finite cylinders; generalised differential quadrature; natural frequency; vibration analysis.

DOI: 10.1504/IJESMS.2013.056691

International Journal of Engineering Systems Modelling and Simulation, 2013 Vol.5 No.4, pp.169 - 173

Published online: 30 Aug 2014 *

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