TY - GEN

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

AU - Tanaka, Toshiyuki

AU - Sato, Chikara

PY - 1993/12/1

Y1 - 1993/12/1

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

T3 - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE

SP - 403

EP - 411

BT - Dynamics and Vibration of Time-Varying Systems and Structures

A2 - Shahinpoor, Mo

A2 - Tzou, H.S.

PB - Publ by ASME

T2 - 14th Biennial Conference on Mechanical Vibration and Noise

Y2 - 19 September 1993 through 22 September 1993

ER -