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The Influence of Modal Geometrical Imperfections on the Nonlinear Vibrations of a Thin-Walled Circular Cylindrical Shell

[+] Author Affiliations
Lara Rodrigues, Paulo B. Gonçalves

Catholic University, Rio de Janeiro, Brazil

Frederico M. A. Silva

Federal University of Goiás, Goiânia, Brazil

Paper No. DETC2016-59649, pp. V008T10A018; 7 pages
doi:10.1115/DETC2016-59649
From:
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 28th Conference on Mechanical Vibration and Noise
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5020-6
  • Copyright © 2016 by ASME

abstract

This work investigates the influence of several modal geometric imperfections on the nonlinear vibration of simply-supported transversally excited cylindrical shells. The Donnell nonlinear shallow shell theory is used to study the nonlinear vibrations of the shell. A general expression for the transversal displacement is obtained by a perturbation procedure which identifies all modes that couple with the linear modes through the quadratic and cubic nonlinearities. The imperfection shape is described by the same modal expansion. So, a particular solution is selected which ensures the convergence of the response up to very large deflections. Substituting the obtained modal expansions into the equations of motions and applying the standard Galerkin method, a discrete system in time domain is obtained. Several numerical strategies are used to study the nonlinear behavior of the imperfect shell. Special attention is given to the influence of the form of the initial geometric imperfections on the natural frequencies, frequency-amplitude relation, resonance curves and bifurcations of simply-supported transversally excited cylindrical shells.

Copyright © 2016 by ASME

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