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

Toshiyuki Tanaka, Chikara Sato

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationAmerican Society of Mechanical Engineers, Design Engineering Division (Publication) DE
EditorsMo Shahinpoor, H.S. Tzou
PublisherPubl by ASME
Pages403-411
Number of pages9
Volume56
ISBN (Print)0791811735
Publication statusPublished - 1993
Event14th Biennial Conference on Mechanical Vibration and Noise - Albuquerque, NM, USA
Duration: 1993 Sep 191993 Sep 22

Other

Other14th Biennial Conference on Mechanical Vibration and Noise
CityAlbuquerque, NM, USA
Period93/9/1993/9/22

Fingerprint

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

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Tanaka, T., & Sato, C. (1993). Stability of the second order difference equation with time-varying parameter. In M. Shahinpoor, & H. S. Tzou (Eds.), American Society of Mechanical Engineers, Design Engineering Division (Publication) DE (Vol. 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. ed. / Mo Shahinpoor; H.S. Tzou. Vol. 56 Publ by ASME, 1993. p. 403-411.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tanaka, T & Sato, C 1993, Stability of the second order difference equation with time-varying parameter. in M Shahinpoor & HS Tzou (eds), American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. vol. 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. In Shahinpoor M, Tzou HS, editors, American Society of Mechanical Engineers, Design Engineering Division (Publication) DE. Vol. 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. editor / Mo Shahinpoor ; H.S. Tzou. Vol. 56 Publ by ASME, 1993. pp. 403-411
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