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

Toshiyuki Tanaka, Chikara Sato

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

Original languageEnglish
Title of host publication14th Biennial Conference on Mechanical Vibration and Noise
Subtitle of host publicationDynamics and Vibration of Time-Varying Systems and Structures
PublisherAmerican Society of Mechanical Engineers (ASME)
Number of pages7
ISBN (Electronic)9780791811733
Publication statusPublished - 1993
EventASME 1993 Design Technical Conferences, DETC 1993 - Albuquerque, United States
Duration: 1993 Sept 191993 Sept 22

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
VolumePart F167972-5


ConferenceASME 1993 Design Technical Conferences, DETC 1993
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modelling and Simulation


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