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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 19
Edited by: B.H.V. Topping
Paper IX.1

Dynamic Response of Large Complex Segmentally Periodic Structures by the Symplectic Matrix Method

M. Zhou* and F.W. Williams+

*Department of Engineering Mechanics, Tsinghua University, Beijing, PR China
+Division of Structural Engineering, School of Engineering, University of Wales College of Cardiff, Wales

Full Bibliographic Reference for this paper
M. Zhou, F.W. Williams, "Dynamic Response of Large Complex Segmentally Periodic Structures by the Symplectic Matrix Method", in B.H.V. Topping, (Editor), "Developments in Computational Engineering Mechanics", Civil-Comp Press, Edinburgh, UK, pp 219-228, 1993. doi:10.4203/ccp.19.9.1
This paper presents a general method which uses the Symplectic Matrix Method to investigate the dynamic response and wave propagation in large complex segmentally periodic structures subjected to external excitations. After the finite element discretization of a typical substructure, the dynamic stiffness matrix is obtained and then converted into a symplectic matrix. Because the eigenvectors of a symplectic matrix are linearly independent, they are taken as a set of co-ordinate vectors and their linear combination is used to express state vector, thus transferring state vectors into wave vectors. The governing equations for wave vectors are derived from the dynamic equilibrium and compatibility conditions at the elastic junctions of the structure. By introducing the boundary conditions at he junctions, wave vectors, and then state vectors, can be found. An example of three segmentally periodic structure is defined as an illustration.

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