P. Sundararajan et St. Noah, DYNAMICS OF FORCED NONLINEAR-SYSTEMS USING SHOOTING ARC-LENGTH CONTINUATION METHOD - APPLICATION TO ROTOR SYSTEMS/, Journal of vibration and acoustics, 119(1), 1997, pp. 9-20
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.