Three-mode interaction in harmonically excited system with cubic nonlinearities

被引：9

作者：

El-Bassiouny, AF ^{[1
]}

机构：

[1] Benha Univ, Fac Sci, Dept Math, Banha 13518, Egypt

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2003年 / 139卷 / 2-3期

关键词：

D O I：

10.1016/S0096-3003(02)00109-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper three-mode interaction in harmonically excited system with cubic nonlinearities to harmonic excitations in the presence of auto-parametric resonances omega(2) congruent to 3omega(1) and omega(3) congruent to 3omega(2) is investigated in two cases. First case, when the amplitudes of external excitation are of order epsilon. Second case, when the amplitudes of external excitation are of order one. The method of multiple scales is used to determine a first-order nonlinear ordinary differential (average) equations governing the modulation of the amplitudes and phases of three modes. Numerical solutions are conducted to obtain the frequency curves of the three modes. The effect of the different parameters on both response and stability of the system is investigated. The obtained results are discussed followed by the main conclusions. (C) 2002 Elsevier Science Inc. All rights reserved.

引用

页码：201 / 230

页数：30

共 23 条

[1]

ATLURI S, 1973, J APPL MECH, V72, P121

[2]

CARTMEL M, 1990, INTRO LINEAR PARAMET

[3] Response of a three-degree-of-freedom system with cubic non-linearities to harmonic excitation [J].