Techno Press
Techno Press

Structural Engineering and Mechanics
  Volume 1, Number 1, October 1993 , pages 47-60
DOI: https://doi.org/10.12989/sem.1993.1.1.047
 

The eigensolutions of wave propagation for repetitive structures
Wanxie Zhong and F.W. Williams

 
Abstract
    The eigen-equation of a wave traveling over repetitive structure is derived directly form the stiffness matrix formulation, in a form which can be used for the case of the cross stiffness submatrix Kab being singular. The weighted adjoint symplectic orthonormality relation is proved first. Then the general method of solution is derived, which can be used either to find all the eigensolutions, or to find the main eigensolutions for large scale problems.
 
Key Words
    repetitive structure; eigenvalue problem; symplectic matrix; wave propagation.
 
Address
Research Institute of Engineering Mechanics, Dalian Univ. of Tech., P.R.C
Division of Structural Engineering, School of Engineering, Univ. of Wales College of Cardiff, U.K.
 
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