Generalized modal reduction method for the dynamic analysis of rotating mechanical systems

Abstract

The paper proposes modal reduction method of the dynamic systems composed of linear nonconservative subsystems coupled by nonlinear discrete couplings. Classical approach to the modal reduction is based on the transformation of the generalized coordinates by the real modal submatrix of the linear conservative part of the whole system. In case of modal synthesis method, transformation matrices are the real modal submatrices of the conservative part of mutually isolated subsystems. Rotating mechanical systems contain gyroscopic effects and other influences of rotation and damping. The paper introduces a generalized modal reduction method based on the complex modal values of the whole system or the isolated subsystems. Their complex eigenvalues and eigenvectors are used for transformation of the generalized coordinates and reduction of the number of degrees of freedom. The presented method is focused on vibrating rotating systems with gyroscopic and dissipative effects and nonlinear internal couplings.

Keywords

• modal reduction method
• complex modal values
• rotating systems
• nonlinear couplings