## Abstract

In the previous paper, an algorithm was presented to obtain the periodic solutions and stability of nonlinear multi-degree-of-freedom systems with high speed and high accuracy, based on the harmonic balance method and the infinitesimal stability criterion. A revised algorithm is presented to give only odd order solutions which are composed of odd order harmonics only, and so reduces the dimensions of the amplitude vector and Jacobian matrix to about one-half of the previous one. The Duffing system with hard spring is analysed by this algorithm and the detailed frequency responses are computed for odd order superharmonic resonances (order 3, 5, 7, 9), which are the odd order solutions. The results are shown for each resonance region in terms of (a) maximum amplitudes and norms, (b) superharmonic amplitudes, (c) fundamental amplitudes, and (d) fundamental and superharmonic phase angles. Some of these are comfirmed by numerical simulation.

Original language | English |
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Pages (from-to) | 1738-1747 |

Number of pages | 10 |

Journal | Nihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C |

Volume | 51 |

Issue number | 467 |

DOIs | |

Publication status | Published - 1985 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Mechanical Engineering
- Industrial and Manufacturing Engineering