中心流形与多变量逼近在非线性稳定性分析中的应用
Center manifold and multivariable approximants applied to non-linear stability analysis
摘要：
本文研究了制动摩擦系数为常数的非线性模型的失稳现象。本文概述了稳定性分析和程序，以减少和简化的非线性系统，以获得极限环振幅。中心流形的方法，多变量逼近理论，和交替的频率/时域（AFT）的方法。制动器振动，更具体地说，重型卡车抓地力是值得关注的。该模型引入了基于动力耦合的拱座滑移机制。非线性度表示为具有二次项和三次项的多项式。该模型不需要使用制动负系数，以预测失稳现象。最后，中心流形方法，多变量逼近，和AFT方法，以获得方程的极限环振幅。这些方法允许减少原始系统的方程的数量，以获得简化的系统，而不失去原始系统的动态，以及非线性项的贡献。我们的目标是验证这个过程中的一个复杂的非线性模型，通过比较通过解决整个系统，并通过使用这些方法得到的结果。制动摩擦系数被用作基本Hopf分岔点的展开参数。
英文摘要：
This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. This paper outlines the stability analysis and a procedure to reduce and simplify the non-linear system, in order to obtain limit cycle amplitudes. The center manifold approach, the multivariable approximants theory, and the alternate frequency/time domain (AFT) method are applied. Brake vibrations, and more specifically heavy trucks grabbing are concerned. The modelling introduces sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the center manifold approach, the multivariable approximants, and the AFT method are used in order to obtain equations for the limit cycle amplitudes. These methods allow the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system, as well as the contributions of non-linear terms. The goal is the validation of this procedure for a complex non-linear model by comparing results obtained by solving the full system and by using these methods. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.
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