A genetic-continuation algorithm for bifurcation analysis of nonlinear rotordynamic systems

Abstract

This study presents a combined numerical scheme with genetic algorithm and continuation method for analysing nonlinear vibrations in rotor-bearing systems. A modified genetic algorithm is developed for solving multiple coexisting roots in nonlinear rotordynamic problem. Here, the genetic objective is the completion of periodicity for the boundary values of journal/pad phase states during the consecutive generations. The arc-length continuation takes the role to extend the solutions with respect to operating parameters such as the shaft spin speed and disc mass eccentricity. The resulting bifurcation diagrams, then, can comprehensively show the emergences and disappearances of multiple response states and their stability conditions in detail, which is unlike with the commonly applied numerical integration method. A finite model of heavily loaded Jeffcott rotor supported by six-pad tilting pad journal bearing is utilized to evaluate the developed algorithm. The 150 initial states for the journal and pad are generated, and the 8 optimal results are selected and inbreeded for evolution; it repeats for 15 generations. As results, multiple coexisting responses are identified at the same condition, and various bifurcation events such as periodic doubling, saddle-node are discovered from the solution manifolds.