Journal
JOURNAL OF VIBRATION AND CONTROL
Volume 18, Issue 11, Pages 1661-1674Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1077546311421053
Keywords
Generalized harmonic balance method; nonlinear oscillator; periodic motions; stability and bifurcation
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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.
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