基于传动带摩擦构建的自激SD振子及其复杂动力学行为研究

Nonlinear friction dynamics is to study the complex nonlinear behaviours and the dynamical responses of the practice system in physics and engineering with friction. Although this research has attracted the world both in academic and engineering for a long period, there is still little desired systematic results appeared in the literature due to the restriction from the conventional theory and the lack of efficiency methodologies, which remains the research on the starting stage. This proposal is to construct a so called self-excited SD oscillator based upon the recent proposed SD oscillator and the relating theory and the experimental investigations, together with the moving belt friction, which is a novel model of nonlinear friction system. The research will be focused on the nonlinear dynamics of the multiple stick-slip motion, friction induced asymmetry and the transition of the hyperbolic structure to derive the characteristics of the special path to chaos and the complex boundary structure of the attraction domains for the coexisted multiple stage attractors. This project will also build up the universal theory for the friction induced asymmetric high codimension bifurcation with multiple parameters and the global dynamical structure with multiple stage limit cycles. Finally, this project is aimed at laying the solid base for engineering applications by demonstrating completely the complex nonlinear behaviour and the dynamical responses of nonlinear self-excited system induced by friction with the help of numerical analysis and experimental investigations.

非线性摩擦动力学是物理与工程等实际非线性系统在摩擦力作用下表现出的复杂非线性动力学特征与响应机理研究。尽管该领域一直受到国内外学者的广泛关注，但由于受传统理论方法的局限、研究工具的缺乏及实验手段滞后的影响，非线性摩擦动力学研究仍处于艰难的起步阶段，文献上很少见到满意的系统性研究成果。本项目基于申请者发现并提出的SD振子及其相应的理论成果与实验手段，并结合传送带摩擦理论方法构建一个称为自激SD振子的非线性摩擦动力学模型，研究摩擦作用下非线性系统出现的多粘滑运动、非对称性以及双曲结构变迁等特有的复杂动力学特征；探讨该系统通向混沌的特殊道路与机理、多吸引子共存条件、规律及其吸引域复杂边界结构特征等；建立摩擦导致的非对称、多参数高余维分岔问题的普适理论并展示极限环分布等全局动力学结构特征；最终结合数值分析和实验手段完整揭示该摩擦自激系统的复杂非线性动力学特征与响应机理，为实际工程应用奠定基础。

本项目构建了基于传送带摩擦的自激SD振子动力学模型，通过理论分析、数值计算和实验手段研究该系统的非线性动力学特性与复杂响应机理。主要研究内容如下：建立了在传送带摩擦驱动下的自激SD振子模型，分析了系统复杂动力学特性，包括不对称性，多粘附特性等。建立了自激SD振子非对称、多参数高余维分岔的识别、分类及普适理论方法；构建了典型的具有几何非线性的准零刚度模型，提出了优化准零刚度隔振器参数和评价其隔振性能的理论和方法；基于一阶近似壳体理论建立转动锥壳的振动控制方程，研究了边界条件、转速和几何特征参数对转动锥壳振动特性的影响；基于具有几何非线性特征的SD振子，提出并研究了有高能量收集效率的多稳态能量采集器。科研成果：发表21篇SCI论文，参加国际会议1次，国内会议8次。培养了6名博士，其中4名在读；12名硕士，其中4名在读。国际合作与交流：与国外知名大学建立了国际合作交流平台，建立广泛的国际合作交流，如南安普顿大学，法国科学院等。邀请到了国际知名学者讲学，包括法国科学院研究院Alain教授，英国南安普顿大学邢景棠教授等。本项目以崭新的研究思路，揭示了具有几何非线性结构的自激SD振子，准零刚度隔振器，薄壳结构，能量采集器等非线性系统的复杂动力学行为演化机理，推动了几何非线性动力学理论及工程应用研究。