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On the direct solution of wave propagation for repetitive structures

✍ Scribed by W.X. Zhong; F.W. Williams

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
592 KB
Volume
181
Category
Article
ISSN
0022-460X

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✦ Synopsis

The direct method of solving the wave constants for a repetitive structure with given frequency v is developed in this paper. The analogy between structural mechanics and optimal control theory is applied. The dynamic stiffness matrix approach is used to solve for the eigensolutions of wave propagation. The weighted adjoint symplectic orthonormality relationship and the eigenvector expansion theorem are also established for this approach. The symplectic eigenproblem is derived for skew-symmetric matrices, a cell triangular decomposition for skew-symmetric matrices is introduced to reduce the generalized eigenproblem, and the symplectic Householder transformation is introduced to cell tri-diagonalize the skew-symmetric matrix to solve the eigenequation. The problem of a wave impinging on the boundary is considered by the eigenvector expansion method, which could also be applied to a wave scattering when passing over an abnormal part. Numerical examples show that resonance will occur for the localized vibration case.

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