Decoupled second-order equations and modal analysis of a general nonconservative system

Abstract

The paper presents the theoretical basis for modal analysis of a general nonconservative system. The modal analysis uses only real modes in terms of the displacements as well as velocity coordinates and converts the system to a real, uncoupled, second-order form. This is the flrst time that such a transformation has been presented in the literature. Earlier works presented modal analysis in the flrst-order state-space, of which, only the gyroscopic conservative system analysis was conducted with real modes. The modal analysis presented herein is a general framework which can be specialized for speciflc systems, e.g., self-adjoint conservative systems or gyroscopic conservative systems. For a self-adjoint conservative system the modal analysis reduces to the normal modal analysis. A byproduct of the modal analysis is the generation of transformations from the original physical coordinates to the real, uncoupled modal space. Such transformations are shown to be quite useful in understanding the behaviour of a nonconservative system. It is used in the present paper to shed light on the destabilizing efiect of damping in circulatory system.