## Abstract

The 1/3 sub-harmonic solution for the Duffing's with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.

Original language | English |
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Pages (from-to) | 1171-1176 |

Number of pages | 6 |

Journal | Applied Mathematics and Mechanics (English Edition) |

Volume | 27 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sept 2006 |

Externally published | Yes |

## Keywords

- Duffing's equation
- Fractal characteristic
- Sensitive dimension
- Sub-harmonic
- Transient process