An Engineering Interpretation of the Complex Eigensolution of Linear Dynamic Systems
IMAC XXIII, www.sem.org, (03.02.2005)Аннотация
In traditional finite element based modal analysis of linear non-conservative structures, the modal shapes are determined solely based on stiffness and mass. Damping effects are included by implicitly assuming that the damping matrix can be diagonalized by the undamped modes. The approach gives real valued mode shapes and modal coordinates. While this framework is suitable for analysis of most lightly damped structural systems, it is insufficient for interpretation of the free vibration and resonant response of structures with e.g. significant non-classical damping, gyroscopic or other effects resulting in a complex eigensolution. In this paper, the more general approach based on complex eigenvalues and eigenvectors is employed. We give an interpretation of the complex eigensolution that describes free and resonant vibrations of a generally damped linear structure. The interpretation show how the different parts of the complex eigensolutions; i.e. the complex left and right eigenvectors together with the complex eigenvalues, combines into vibration frequencies and modal damping ratios, mode shape magnitudes and phase angles, and modal coordinate magnitude and phase angles. The presented interpretation relates all elements of the complex valued solution to physical quantities that are well known in structural dynamics as well as other fields studying linear dynamic systems, and complements the already applied interpretations.