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A New Nonlinear Higher-Order Shear Deformation Theory for Nonlinear Vibrations of Laminated Shells

[+] Author Affiliations
M. Amabili

McGill University, Montreal, QC, Canada

J. N. Reddy

Texas A&M University, College Station, TX

Paper No. IMECE2010-39483, pp. 1017-1025; 9 pages
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 8: Dynamic Systems and Control, Parts A and B
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4445-8
  • Copyright © 2010 by ASME


A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape; taking geometric imperfections into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only nonlinear terms of the von Kármán type. Results show that inaccurate results are obtained by keeping only nonlinear terms of the von Kármán type for vibration amplitudes of about two times the shell thickness for the studied case.

Copyright © 2010 by ASME



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