### Abstract

This paper deals with the stability of the second order difference equation possessing periodic parameter, which characterizes discrete periodic system. Discrete periodic system corresponding to Mathieu equation is expressed as second order difference equation with small parameter ε in the time-varying term. This parameter ε plays an important role in stability. For the fundamental equation without damping, stability boundary curves are analytically obtained with respect to parameters in the equation by using McLachlan's method, which is based on Floquet's theory and perturbation method. The boundary curves are computed by pursuing periodic solutions on the boundaries and letting secular term zero. The boundary curves are expressed as the power series of ε. When periodic parameter consists of even function of Fourier series, stability boundary curves are obtained. For the fundamental equation with damping, stability criterion is shown in the neighbor of important resonant points. This criterion is obtained by computing points on the boundary curves.

Original language | English |
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Title of host publication | Dynamics and Vibration of Time-Varying Systems and Structures |

Editors | Mo Shahinpoor, H.S. Tzou |

Publisher | Publ by ASME |

Pages | 403-411 |

Number of pages | 9 |

ISBN (Print) | 0791811735 |

Publication status | Published - 1993 Dec 1 |

Event | 14th Biennial Conference on Mechanical Vibration and Noise - Albuquerque, NM, USA Duration: 1993 Sep 19 → 1993 Sep 22 |

### Publication series

Name | American Society of Mechanical Engineers, Design Engineering Division (Publication) DE |
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Volume | 56 |

### Other

Other | 14th Biennial Conference on Mechanical Vibration and Noise |
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City | Albuquerque, NM, USA |

Period | 93/9/19 → 93/9/22 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Dynamics and Vibration of Time-Varying Systems and Structures*(pp. 403-411). (American Society of Mechanical Engineers, Design Engineering Division (Publication) DE; Vol. 56). Publ by ASME.