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Nonlinear Vibrations of Cantilever Circular Cylindrical Shells

[+] Author Affiliations
M. Amabili

McGill University, Montreal, QC, Canada

Ye. Kurylov

Università degli Studi di Parma, Parma, Italy

Paper No. DETC2010-28484, pp. 851-858; 8 pages
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4413-7 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME


Only experimental studies are available on large amplitude vibrations of cantilever shells. In the present paper, large-amplitude nonlinear vibrations of cantilever circular cylindrical shell are investigated. Shells with perfect and imperfect shape are studied. The Sanders-Koiter nonlinear shell theory, which includes shear deformation, is used to calculate the elastic strain energy. Shell’s displacement fields (longitudinal, circumferential and radial) are expanded by means of a double mixed series: harmonic functions for the circumferential variable; Chebyshev polynomials for the longitudinal variable. Boundary conditions are exactly satisfied. The Lagrangian approach is applied to obtain a system of nonlinear ordinary differential equations. The nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis. Numerical responses in the spectral neighborhood of the lowest natural frequency are obtained.

Copyright © 2010 by ASME



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