### 抄録

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.

元の言語 | English |
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ホスト出版物のタイトル | American Society of Mechanical Engineers, Design Engineering Division (Publication) DE |

編集者 | Mo Shahinpoor, H.S. Tzou |

出版者 | Publ by ASME |

ページ | 403-411 |

ページ数 | 9 |

巻 | 56 |

ISBN（印刷物） | 0791811735 |

出版物ステータス | Published - 1993 |

イベント | 14th Biennial Conference on Mechanical Vibration and Noise - Albuquerque, NM, USA 継続期間: 1993 9 19 → 1993 9 22 |

### Other

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

期間 | 93/9/19 → 93/9/22 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### これを引用

*American Society of Mechanical Engineers, Design Engineering Division (Publication) DE*(巻 56, pp. 403-411). Publ by ASME.

**Stability of the second order difference equation with time-varying parameter.** / Tanaka, Toshiyuki; Sato, Chikara.

研究成果: Conference contribution

*American Society of Mechanical Engineers, Design Engineering Division (Publication) DE.*巻. 56, Publ by ASME, pp. 403-411, 14th Biennial Conference on Mechanical Vibration and Noise, Albuquerque, NM, USA, 93/9/19.

}

TY - GEN

T1 - Stability of the second order difference equation with time-varying parameter

AU - Tanaka, Toshiyuki

AU - Sato, Chikara

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0027801709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027801709&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027801709

SN - 0791811735

VL - 56

SP - 403

EP - 411

BT - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE

A2 - Shahinpoor, Mo

A2 - Tzou, H.S.

PB - Publ by ASME

ER -