Bifurcation tracking of geared systems with parameter-dependent internal excitation

We herein propose an algorithm for tracking smooth bifurcations of nonlinear systems with interdependent parameters. The approach is based on a complex formulation the well-known harmonic balance method (HBM). Hill’s used to assess stability computed forced response curves, and minimally extended system built allow parametric continuation detected bifurcation points. feasibility coupling HBM-based arc-length algorithms established demonstrated. offers efficient way determining regions system. methodology applied spur gear pair model including backlash nonlinearity subjected transmission error mesh stiffness fluctuation whose contents depend several parameters that do not appear explicitly in equations motion.