Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance

作者：Luo Albert C J^*; Huang Jianzhe

来源：Journal of Vibration and Control, 2012, 18(11): 1661-1674.

DOI：10.1177/1077546311421053

• Generalized harmonic balance method
• nonlinear oscillator
• periodic motions
• stability and bifurcation

In this paper, the generalized harmonic balance method is presented for approximate, analytical solutions of periodic motions in nonlinear dynamical systems. The nonlinear damping, periodically forced, Duffing oscillator is studied as a sample problem. The approximate, analytical solution of period-1 periodic motion of such an oscillator is obtained by the generalized harmonic balance method. The stability and bifurcation analysis of the HB2 approximate solution of period-1 motions in the forced Duffing oscillator is carried out, and the parameter map for such HB2 solutions is achieved. Numerical illustrations of period-1 motions are presented. Similarly, the same ideas can be extended to period-k motions in such an oscillator. The methodology presented in this paper can be applied to other nonlinear vibration systems, which are independent of small parameters.

• 出版日期2012-10