A Bernoulli-Euler Stiffness Matrix Approach for Vibrational Analysis of Spinning Linearly Tapered Beams FREE

[+] Author Affiliations
S. M. Hashemi, M. J. Richard

Laval University, Québec, QC, Canada

G. Dhatt

Institut de Mecanique de Rouen, l’INSA de Rouen, Mont Saint Aignan, France

Paper No. 97-GT-500, pp. V004T14A067; 6 pages
  • ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition
  • Volume 4: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award
  • Orlando, Florida, USA, June 2–5, 1997
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-7871-2
  • Copyright © 1997 by ASME


This paper presents a Dynamic Finite Element (DFE) formulation, based on the Dynamic Stiffness Matrix (DSM) approach, for vibrational analysis of spinning beams. The constituent members are considered to be linearly tapered as well as centrifugally stiffened. A non-dimensional formulation is considered, and the frequency dependent trigonometric shape functions are used to find a single frequency dependent element matrix (called DSM) which has both mass and stiffness properties. An adapted bisection method based on a Sturm sequence root counting technique, is used to find the first four out-of-plane flexural natural frequencies of a cantilevered linearly tapered (in height) beam for different non-dimensional rotating speeds. The results have been compared to those found by finite elements method using Hermite beam elements. Much better convergency rates are found by this method when comparing to conventional finite element methods.

Copyright © 1997 by ASME
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