A PERTURBATION METHOD FOR THE ANALYSIS OF VIBRATIONS AND BIFURCATIONS ASSOCIATED WITH NONAUTONOMOUS SYSTEMS .1. NONRESONANCE CASE

A new perturbation technique, based on the intrinsic harmonic balancing and time scaling, is developed for the analysis of vibration and bifurcation problems associated with non-autonomous systems. The method combines selected features of the intrinsic harmonic-balancing technique (introduced earlier) and multiple-time-scaling in an effort to produce a more efficient procedure for non-linear analyses. Both non-resonance (part I) and resonance (part II) cases are treated from a unified point of view. The method is first described on one-degree-of-freedom systems, and then generalized to higher dimensional systems. The application of the technique to specific problems is illustrated on several examples. In particular, the problem of perturbed Hopf bifurcations arising in non-autonomous systems is analysed in general terms such that the results are applicable to all specific problems within the scope of the general formulation.