Computation of Gyroscopic Systems and Symplectic Eigenproblems of Skew-symmetric Matrices

Authors

Wanxie Zhong, Dalian University of Technology,
J. Lin, Dalian University of Technology
Jianping Zhu, Cleveland State UniversityFollow

Document Type

Article

Publication Date

9-3-1994

Publication Title

Computers and Structures

Abstract

The generalized eigenproblem of a linear gyroscopic system with a non-positive definitive stiffness matrix K is derived based on the state vector method. The expansion theorem for an arbitrary state vector and the weighted adjoint symplectic orthogonality between eigenvectors are also proved in the paper. By using the symplectic LDL^T factorization, the generalized eigenproblem is reduced to the standard form of symplectic eigenproblem of skew-symmetric matrices. The symplectic orthogonal transformations are then used to tri-diagonalize the coefficient matrix for the solutions of eigenvalues and eigenvectors which is the central part of modal analysis for gyroscopic systems.

Repository Citation

Zhong, W., Lin, J., and Zhu, J. (1994). Computation of Gyroscopic Systems and Symplectic Eigenproblems of Skew-symmetric Matrices. International Journal of Computers and Structures, 52, 999-1009.

Original Citation

Zhong, W., Lin, J., and Zhu, J. (1994). Computation of Gyroscopic Systems and Symplectic Eigenproblems of Skew-symmetric Matrices. International Journal of Computers and Structures, 52, 999-1009.

DOI

0.1016/0045-7949(94)90084-1

Volume

52

Issue

5