Effect of Damping on Asymmetric Systems

Abstract

This paper addresses the phenomenon of the destabilizing effect of slight damping on asymmetric linear systems. Previous works had showed that the destabilizing effect, regarded for a long time as a “paradox,” depends upon the ratio of the damping coefficients. This work extends those results to n-dof systems. In fact, conditions for a general asymmetric n-dof slightly damped system to be stable are obtained. Also, a useful sufficient condition is carried out. This practical design tool gives optimum damping ratios and takes into consideration the parameter uncertainties as well. The solution is based on the eigenvalue sensitivity analysis. Moreover, a formal physical explanation of the destabilizing effect of damping is given. Eventually, the theory is validated by means of a simple example.