Generalized modal reduction method for the dynamic analysis ofrotating mechanical systems

Abstract

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