Vol. 5, No. 6, 2010

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ISSN: 1559-3959
On the nonlinear dynamics of oval cylindrical shells

Syed Muhammad Ibrahim, Badri Prasad Patel and Yogendra Nath

Vol. 5 (2010), No. 6, 887–908
Abstract

The nonlinear periodic response characteristics of symmetrically and nonsymmetrically excited oval cylindrical shells are investigated using the first order shear deformation theory based finite strip method. The periodic solutions of the governing second order equations of motion are obtained using the shooting technique coupled with Newmark time marching and the arc length continuation algorithm. The effect of ovality parameter and loading locations on the steady state frequency response and modal participation factors is studied. For circular shells (ζ = 0.0), travelling waves emanating at loading point but moving in opposite directions for certain range of forcing frequency are brought out. For the symmetrically excited oval shell with ζ = 0.6, due to 1:1 internal resonance between the AS/SS and SA/AA modes, a secondary branch with traveling wave response emanates from the primary one through a symmetry breaking bifurcation. For the nonsymmetrically excited oval shells (ζ = 0.6), either waves moving in anticlockwise direction or those originating near the major axis and moving in opposite directions in the top and bottom halves of the shell are observed for certain forcing frequency ranges.

Keywords
noncircular shell, nonlinear, periodic, shooting, travelling wave, internal resonance
Milestones
Received: 28 January 2010
Revised: 29 April 2010
Accepted: 8 May 2010
Published: 1 January 2011
Authors
Syed Muhammad Ibrahim
Department of Applied Mechanics
Indian Institute of Technology Delhi
Hauz Khas
New Delhi 110016
India
Badri Prasad Patel
Department of Applied Mechanics
Indian Institute of Technology Delhi
Hauz Khas
New Delhi 110016
India
Yogendra Nath
Department of Applied Mechanics
Indian Institute of Technology Delhi
Hauz Khas
New Delhi 110016
India