SINGULAR CHARACTERISTICS OF NONLINEAR NORMAL MODES IN A TWO DEGREES OF FREEDOM ASYMMETRIC SYSTEMS WITH CUBIC NONLINEARITIES

徐鉴; 陆启韶; 黄克累

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SINGULAR CHARACTERISTICS OF NONLINEAR NORMAL MODES IN A TWO DEGREES OF FREEDOM ASYMMETRIC SYSTEMS WITH CUBIC NONLINEARITIES

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摘要

Nonlinear normal modes in a two degrees of freedom asymmetric system with cubic nonlinearities as singularity occurs in the system are studied, based on the invariant space in nonlinear normal modes and perturbation technique. Emphasis is placed on singular characteristics as the linear coupling between subsystems degenerated. For non_ resonances, it is analytically presented that a single_mode motion and localization of vibrations occur in the system, and the degree of localization relates not only to the coupling stiffness between oscillators, but also to the asymmetric parameter. The parametric threshold value of localization is analytically given. For 1∶1 resonance, there exist bifurcations of normal modes with nonlinearly coupling stiffness and asymmetric parameter varying. The bifurcating set on the parameter and bifurcating curves of normal modes are obtained.

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《应用数学和力学：英文版》 |2001年第8期|972-982|共11页
作者
徐鉴; 陆启韶; 黄克累;
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作者单位

Department of Engineering Mechanics and Technology;

Tongji University;

Shanghai 200092;

P R China;

Department of Applied Mathematics;

Beijing University of Aeronautics and Astronautics;

Beijing 100083;

P R China;

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原文格式 PDF
正文语种 chi
中图分类非线性振动;结构力学;
关键词
asymmetric; system; nonlinear; normal; mode; localization; of; vibration; bifurcation; of; normal; mode; nonlinear; dynamics;

机译：非对称系统;非线性标准模式;振动局部化;标准模式的分叉;非线性动力学;

SINGULAR CHARACTERISTICS OF NONLINEAR NORMAL MODES IN A TWO DEGREES OF FREEDOM ASYMMETRIC SYSTEMS WITH CUBIC NONLINEARITIES

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