摘要
本文主要是从非线性振动的角度出发综述了近年来国内外在非线性振动、分叉和混沌理论及其应用方面的主要成果和发展前景。首先,本文回顾了非线性振动理论的历史,阐述了应用分叉和混沌理论研究非线性振动系统的必要性,进而给出了近期非线性振动八个重点方面的研究方向。其次,我们详细地综述了非线性振动系统的解析方法、非线性振动系统的局部分叉理论及分析方法、非线性振动系统的全局分叉及混沌、非线性随机系统的振动与分叉理论四个方面近期国内外研究工作的主要成果和进展。最后,本文说明了今后分叉和混沌及其应用于非线性振动的主要研究内容。
This paper,starting from nonlinear vibration,summarizes the principal achievements on theory and ap-plications of bifurcation and chaos in nonlinear vibration in recent years,and the prospects for them athome and abroad.Firstly,the paper reviews the history of the development in theory of nonlinear vibra-tion,expounds the necessity that the modern theory of bifurcation and chaos is applied to research nonlin-ear vibrant systems.Moreover,eight important orientations of studying nonlinear vibration are given.In ad-dition,it describes fully the main results and developments of the researching works at home and abroad infour aspects:analytic methods of nonlinear vibrant systems,theory and analytic methods of local bifurca-tion of nonlinear vibration systems,global bifurcation and chaos of nonlinear vibrant systems,and theory ofvibration and bifurcation in nonlinear stochastic systems.Finally,the paper describes the main content infuture research of theory of bifurcation and chaos,and its applications in nonlinear vibration.
出处
《振动工程学报》
EI
CSCD
1992年第3期235-250,共16页
Journal of Vibration Engineering
基金
国家自然科学基金
博士点基金的部分资助课题
关键词
非线性振动
分叉
混沌
随机系统
nonlinear vibration
bifurcation
chaos
nonlinear stochastic system
