Nonlinear Dynamics in Mechanical Systems

本项目利用动力系统理论的最新发展来分析工程动力学问题。具体来说，局部和全局分岔技术用于预测动力学行为作为系统参数的函数，以及描述它们。主要研究了四类系统，包括使用输入波形来抑制周期性强迫振荡器中的混沌，具有混沌动力学的主动模态的系统中静止模态的稳定性，旋转机械系统中的非线性动态相互作用，并建立了具有柔性连杆机构动力响应的简单模型。近年来，非线性动力学领域的理论发展与应用之间的差距越来越大。这项研究是通过在具体机械系统的研究中采用现代分析和数值工具来弥合这一差距的直接尝试。

This project utilizes recent developments in dynamical systems theory in the analysis of engineering dynamics problems. Specifically, local and global bifurcation techniques are used to predict dynamics behavior as a function of system parameters, as well as to describe them. The research focuses on four classes of systems, including the use of input waveform for the suppression of chaos in periodically forced oscillators, the stability of modes at rest in systems which have active modes undergoing chaotic dynamics, nonlinear dynamic interactions in rotating mechanical systems, and simple models for the dynamic response of mechanisms with flexible linkages. A widening gap between theoretical developments and applications in the field of nonlinear dynamics has occurred in recent years. This research is a direct attempt to bridge that gap by employing modern analytical and numerical tools in the investigation of specific mechanical systems.