Stability conditions for non-conservative dynamical systems

The present paper treats dynamic instability problems of non-conservative elastic systems. Starting from general equations of motion, the equations of the perturbed motion are derived. The boundedness of the perturbed motions is studied and sufficient conditions for instability and a necessary condition for stability are deduced. These conditions may determine the instability of non-conservative systems and they are expressed in terms of the properties of generalized tangent damping and stiffness matrices of the systems. Thus, they can easily be incorporated with finite element computations of arbitrary structures.