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Free Vibration Analysis of Rotating Structures by One-Dimensional, Variable Kinematic Theories

[+] Author Affiliations
Erasmo Carrera, Matteo Filippi, Enrico Zappino

Politecnico di Torino, Torino, Italy

Paper No. IMECE2013-63183, pp. V009T10A021; 10 pages
doi:10.1115/IMECE2013-63183
From:
  • ASME 2013 International Mechanical Engineering Congress and Exposition
  • Volume 9: Mechanics of Solids, Structures and Fluids
  • San Diego, California, USA, November 15–21, 2013
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5638-3
  • Copyright © 2013 by ASME

abstract

In this paper, Carrera’s Unified Formulation (CUF) is extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor’s polynomials of N-order, in which N is a free parameter. The linear case (N = 1) permits us to obtain classical beam theories while higher order expansions could lead to three-dimensional description of dynamic response of both rotors and centrifugally stiffened beams. The Finite Element method is used to derive the weak form of the three-dimensional differential equations of motion in term of fundamental nuclei, whose forms do not depend on the approximation used (N). The present formulations include gyroscopic effects and stiffening due to centrifugal stresses. In order to verify the accuracy of the new theories, several analyses are carried out and the results are compared with solutions presented in the literature in graphical and numerical form. The advantages of the variable kinematic models are evident especially when shafts with deformable discs and thin-walled rotating beams made up with composite materials are studied.

Copyright © 2013 by ASME

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