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The harmonic balance (HB) method is widely used in the literature foranalyzing the periodic solutions of nonlinear mechanical systems. The objectiveof this paper is to exploit the method for bifurcation analysis, i.e., for thedetection and tracking of bifurcations of nonlinear systems. To this end, analgorithm that combines the computation of the Floquet exponents with borderingtechniques is developed. A new procedure for the tracking of Neimark-Sackerbifurcations that exploits the properties of eigenvalue derivatives is alsoproposed. The HB method is demonstrated using numerical experiments of aspacecraft structure that possesses a nonlinear vibration isolation device.

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems