Symplectic Integration and Nonlinear Dynamic Symmetry Breaking of Frames | Zendy

Shenggen Mao | Zendy; A.Y.T. Leung | Zendy

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Symplectic Integration and Nonlinear Dynamic Symmetry Breaking of Frames

Author(s) -

Shenggen Mao,

A.Y.T. Leung

Publication year - 1995

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/1995/671835

Subject(s) - symplectic geometry , nonlinear system , invariant (physics) , vibration , finite element method , structural engineering , stiffness , hamiltonian (control theory) , beam (structure) , symplectic integrator , mathematics , classical mechanics , mathematical analysis , physics , engineering , symplectic manifold , mathematical physics , mathematical optimization , quantum mechanics

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.

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