Conditions for the occurrence of limit cycles in autonomous potential damped systems

The focal dynamic stability of discrete, weakly damped, systems under step loading of infinite duration either constant directional (potential load) o r partial follower (non-potential load) is thoroughly re-examined. In parti cular, for such autonomous damped systems we seek conditions for the existe nce of: (a) a limit cycle response in case of a potential loading (symmetri c) system and (b) a non-singular transformation which transforms a non-pote ntial (asymmetric) system into an equivalent symmetric system. Using a 2-DO F as a model new findings are established that contradict existing widely a ccepted results. Thus, symmetric systems under certain conditions can exhib it a limit cycle response due to either a double-zero Jacobian eigenvalue o r to a Hopf bifurcation. Also asymmetric (non-self-adjoint) systems, regard less of the degree of asymmetry, can always be transformed into equivalent symmetric systems. A variety of numerical examples confirm the validity of the theoretical findings presented herein. (C) 1999 Elsevier Science Ltd. A ll rights reserved.