AN ALGORITHM FOR RESPONSE AND STABILITY OF LARGE-ORDER NONLINEAR-SYSTEMS - APPLICATION TO ROTOR SYSTEMS

A numerical algorithm to calculate the periodic response, stability an d bifurcations of a periodically excited non-conservative, Multi-Degre e of Freedom (MDOF) system with strong local non-linearities is presen ted. First, the given large order system is reduced using a fixed-inte rface component mode synthesis procedure (CMS) in which the degrees of freedom associated with non-linear elements are retained in the physi cal co-ordinates while all others, whose number far exceeds the number of non-linear DOF, are transformed to modal co-ordinates and reduced using real mode CMS. A shooting and continuation method is then applie d to the reduced system to solve for the periodic response. Floquet st ability theory is used to calculate stability and bifurcations of the periodic response. The algorithm is applied to study the response to i mbalance, stability, and bifurcations of a 24 DOF flexible rotor suppo rted on journal bearings. The results indicate that the proposed algor ithm, though approximate, can yield very accurate information about dy namic behavior of large order non-linear systems, even with few number s of retained component modes. The algorithm, which imposes less deman d on computer time and memory, is believed to be of considerable poten tial in analyzing a variety of practical problems. (C) 1998 Academic P ress.