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

Toshiyuki Tanaka, Chikara Sato

研究成果: Conference contribution


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 £ in the time-varying term. This parameter e 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 e. 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.

ホスト出版物のタイトル14th Biennial Conference on Mechanical Vibration and Noise
ホスト出版物のサブタイトルDynamics and Vibration of Time-Varying Systems and Structures
出版社American Society of Mechanical Engineers (ASME)
出版ステータスPublished - 1993
イベントASME 1993 Design Technical Conferences, DETC 1993 - Albuquerque, United States
継続期間: 1993 9月 191993 9月 22


名前Proceedings of the ASME Design Engineering Technical Conference
Part F167972-5


ConferenceASME 1993 Design Technical Conferences, DETC 1993
国/地域United States

ASJC Scopus subject areas

  • 機械工学
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • コンピュータ サイエンスの応用
  • モデリングとシミュレーション


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