摘要
本论文研究了一类干摩擦系统的动力学行为及其周期运动的稳定性,主要有以下内容:
第一章介绍了干摩擦系统研究的现状与取得的成果,及其所涉及的一些基本概念,譬如分界面、擦边分岔等;还阐述了非光滑系统周期运动稳定性研究的基本方法。
第二章讨论了干摩擦力的非线性特性,随后建立了一类两自由度干摩擦模型,着重研究该两自由度干摩擦系统的动力学特性。文中列出了系统处于纯黏附、纯滑移及半黏附状态时的判定条件,并给出了对应于不同状态时系统的运动微分方程。
第三章应用Floquet理论研究了处于纯滑移状态干摩擦系统的周期运动稳定性。首先研究了处于纯滑移状态时单自由度线性干摩擦系统周期运动的稳定性;接着,再将研究方法推广到两自由度系统,根据相轨线穿越分界面的情况,本文将两自由度线性干摩擦系统分为三类,即无穿越系统、单穿越系统及双穿越系统,随后对此三类系统逐个进行稳定性研究;最后,还简要介绍了在纯滑移状态下非线性干摩擦系统周期运动稳定性的研究方法。
第四章利用MATLAB软件对以上干摩擦系统进行数值仿真,数值模拟了处于黏附状态与滑移状态系统的周期运动,得到了处于纯滑移状态系统周期运动的相图,并对其进行了稳定性判定。
In this paper, we study the dynamics behavior and the periodic motion of a dry friction system. The contents are listed as follows:
In Chapter 1, we introduce the present situation and the achievement about the study of the system with dry friction, which involve some basic concepts, such as the switch boundary, grazing bifurcation. Besides, we elaborate the general method for studying the stability of the periodic motion in non-smooth system.
In Chapter 2, we analyze the nonlinear characteristic of the dry friction, and then set up the model of a two-degree-of-freedom system with dry friction. Our studying will focus on the dynamics characteristic of the system. We list the conditions about the full stick state, full slip state, half stick state, and establish the differential equations which correspond with the studied system.
In Chapter 3, we study the stability of the periodic motion of the system with dry friction under the full slip state with the help of Floquet Theory. Firstly we study the stability of the periodic motion of one-degree-of-freedom system with linear dry friction under the full slip state. Then we extend the study to two-degree-of-freedom system. According to the relation how the trajectories pass the switch boundaries, the periodic motion of two-degree-of-freedom system with dry friction can be classified into three kinds, which are denominated as not-crossing, single-crossing, double-crossing cases in this paper. Subsequently, we give the examples them and study the stability of them respectively. Finally, we briefly introduce the methods to study the stability of periodic motion of the system with non-linear dry friction under the full slip state.
In Chapter 4, by means of MATLAB we carry out the numerical simulation of the system with dry friction we have mentioned above, and obtain the phase portraits of periodic motion in the system under the stick state or slip state. In addition, we get the phase portraits of periodic motion under the full slip state, and analyze their stability.
引文
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