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

Toshiyuki Tanaka, Chikara Sato

研究成果: Conference contribution

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
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
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 191993 9 22

Other

Other14th Biennial Conference on Mechanical Vibration and Noise
Albuquerque, NM, USA
期間93/9/1993/9/22

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Convergence of numerical methods
Difference equations
Time varying systems
Damping
Fourier series
Stability criteria

ASJC Scopus subject areas

  • Engineering(all)

これを引用

Tanaka, T., & Sato, C. (1993). Stability of the second order difference equation with time-varying parameter. : M. Shahinpoor, & H. S. Tzou (版), 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.

American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. 版 / Mo Shahinpoor; H.S. Tzou. 巻 56 Publ by ASME, 1993. p. 403-411.

研究成果: Conference contribution

Tanaka, T & Sato, C 1993, Stability of the second order difference equation with time-varying parameter. : M Shahinpoor & HS Tzou (版), 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.
Tanaka T, Sato C. Stability of the second order difference equation with time-varying parameter. : Shahinpoor M, Tzou HS, 編集者, American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. 巻 56. Publ by ASME. 1993. p. 403-411
Tanaka, Toshiyuki ; Sato, Chikara. / Stability of the second order difference equation with time-varying parameter. American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. 編集者 / Mo Shahinpoor ; H.S. Tzou. 巻 56 Publ by ASME, 1993. pp. 403-411
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