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Shock and Vibration
Volume 2 (1995), Issue 6, Pages 481-492

Symplectic Integration and Nonlinear Dynamic Symmetry Breaking of Frames

S.G. Mao and A.Y.T. Leung

Department of Civil and Structural Engineering, University of Hong Kong, Hong Kong

Received 25 July 1994; Accepted 15 May 1995

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An accurate beam finite element is used to solve nonlinear vibration of arched beams and framed structures. The nonlinear governing equations of a skeletal structure are integrated numerically using symplectic integration schemes so that the Poincaré integral invariant of a Hamiltonian flow are preserved during the evolution. The element stiffness matrices are not required to be assembled into global form, because the integration is completed on an element level so that many elements can be handled in core by a small computer. Testing examples include arched beams and frames with and without damping in free and forced vibration. The dynamic symmetry breaking phenomena are noted at the dynamic buckling point.