Damping-Induced Stability Transitions in Non-Conservative Systems: New Thoughts on an Old Paradox

Abstract It is well known that non-conservative systems can become unstable when the level of damping is increased. Systems which become stable at higher levels of damping have also been demonstrated along with the phenomenon of three stability transitions that recently appeared in the literature. This work highlights the role of damping on a two-link system subjected to non-conservative force. The addition of damping can cause the non-conservative systems to become stable, then unstable, then stable again at the same value of the non-conservative forcing. This stability transitions is located by application of the Routh-Hurwitz criterion two times, back-to-back, once for the characteristic polynomial and the second time for the polynomial that guarantees the existence of a second-order auxilliary polynomial in the Routh array.