DYNAMICS OF FORCED NONLINEAR-SYSTEMS USING SHOOTING ARC-LENGTH CONTINUATION METHOD - APPLICATION TO ROTOR SYSTEMS/

The analysis of systems subjected to periodic excitations can be highl y complex in the presence of strong nonlinearities. Nonlinear systems exhibit a variety of dynamic behavior that includes periodic, almost-p eriodic (quasi-periodic), and chaotic motions. This paper describes a computational algorithm based on the shooting method that calculates t he periodic responses of a nonlinear system under periodic excitation. The current algorithm calculates also the stability of periodic solut ions and locates system parameter ranges where aperiodic and chaotic r esponses bifurcate from the periodic response. Once the system respons e for a parameter is known, the solution for near range of the paramet er is calculated efficiently using a pseudo-are length continuation pr ocedure. Practical procedures for continuation, numerical difficulties and some strategies for overcoming them are also given. The numerical scheme is used to study the imbalance response of a rigid rotor suppo rted on squeeze-film dampers and journal bearings, which have nonlinea r stiffness and damping characteristics. Rotor spinning speed is used as the bifurcation parameter, and speed ranges of sub-harmonic, quasi- periodic and chaotic motions are calculated for a set of system parame ters of practical interest. The mechanisms of these bifurcations also are explained through Floquet theory, and bifurcation diagrams.