非线性动力学理论及其在机械系统中应用的若干进展

非线性动力学的理论及其工程应用是非线性科学研究的前沿和热点，应用非线性动力学的理论揭示事物动态过程现象的本质和机理，进行自主性原始创新，具有十分重大的理论和应用价值，在科学与工程中具有广阔的应用前景。综述非线性动力学基础理论方面的近期研究成果及其在机械系统中应用的研究进展。理论研究方面主要涉及揭示非线性动力系统周期分岔解与系统结构参数之间关系的C—L方法、高余维分岔的普适分类、高余维非对称分岔的普适开折、约束分岔的分类、计算非线性自治系统正规形的直接方法、计算非线性非自治系统正规形的复内积平均法以及高维非线性系统的降维方法等。应用方面主要涉及大型旋转机械非线性转子系统的失稳机理、分岔解与混沌运动、故障诊断及其综合治理技术；冲击振动机械的稳定性、Hopf分岔、亚谐分岔、余维二分岔和混沌运动；大型共振筛的非线性振动及其动力学设计方法等。

Recent Developments in Nonlinear Dynamics: Theory and Its Applications in Mechanical Systems

Theoretical analysis of nonlinear dynamics and its applications in engineering pioneers the major research issues in nonlinear science. It has significant values in both theory and applications to do innovative research and to reveal the essential features and mechanism of dynamic processes of complex systems utilizing the theory of nonlinear dynamics. The results and achievements in nonlinear dynamics will be widely used in science and engineering. This paper is an attempt to categorize recent research achievements in fundamental theory of nonlinear dynamics and its applications in mechanical systems. In aspect of theoretical research, the major issues concerned are the Chen-Longford method that reveals the important relation between the periodic bifurcation solutions of nonlinear dynamical systems and the structural parameters of the system, universal classification of high co-dimension bifurcations, universal unfolding of high co-dimension unsymmetrical bifurcations, classification of constraint bifurcations, the direct method for calculating the normal form of nonlinear autonomous systems, the complex inner product averaging method for calculating the normal form of nonlinear non-autonomous systems, and the order reduction methods for high dimensional systems. In aspect of applications, the major topics concerned are the instability mechanism, bifurcation solutions, chaotic motions, fault diagnosis and its synthetic control techniques of the nonlinear rotor dynamical systems for large-scale rotating machinery; the stability, Hopf bifurcation, subharmonic bifurcations, co-dimension 2 bifurcation, and chaotic motions of impact-vibrating systems; and the dynamic design strategy and nonlinear vibrations of large-scale resonant screens.