准零刚度隔振系统混沌化技术研究

It is well known that the acoustic stealthy of submarine is difficult to be ensured because the output spectrum structure of general vibration isolation system is steady and the isolation of mechanical low-frequency vibration is tough to be achieved, which leads to being detected, identified and tracked easily by enemy sonar. Concerning the mentioned problems, the chaotification of the quasi-zero-stiffness isolation system is studied. The low-frequency vibration can be isolated effectively with the application of the quasi-zero-stiffness system, and the output spectrum is changed when the system is chaotic. The research is carried out in several parts. The general theoretical model of quasi-zero-stiffness isolation system in submarine’s mechanical equipment is to be established. Based on this model, the coupling characteristics between nonlinear positive and negative structures and rules in modes energy exchange are researched. Furthermore, the global dynamical perturbation, which is suitable for quasi-zero-stiffness isolation system under multi-frequency excitation, is be developed based on differential geometry theory and generalized Melnikov method. The principle resonance, subharmonic resonance, ultra harmonic resonance and possibly internal resonance are illustrated through the global character analysis. In order to realized the quasi-zero-system isolation system chaotification, the generalized chaotic synchronization is studied, as a result, multi-stable synchronization manifold and synchronization waveform conditions are obtained.

针对潜艇机械设备低频振动难以隔离以及常用隔振系统输出频谱结构稳定，容易被敌方声纳探测、识别和跟踪，给潜艇声隐身性能构成威胁的问题，本项目对准零刚度隔振系统混沌化技术开展研究，通过准零刚度隔振系统对低频振动进行有效隔离，通过准零刚度隔振系统混沌化改变输出频谱结构，降低线谱强度。主要内容包括建立潜艇机械设备准零刚度隔振系统一般理论模型，研究非线性正、负刚度机构耦合特性和模态之间能量交换的规律；基于微分几何理论、广义Melnikov方法等，发展适用于研究准零刚度系统在多频激励下的全局动力学摄动法，并对系统的全局特性进行研究，揭示系统的主共振、次谐波共振、超谐波共振以及可能存在的内共振特性规律；研究准零刚度隔振系统广义混沌同步化方法，对系统混沌同步的稳定性和多稳定同步流形进行分析，获得同步流形的条件，实现准零刚度隔振系统混沌化，从而改变输出频谱特征。

本项目将混沌动力学与潜艇动力机械隔振这一工程领域相结合，针对潜艇安装空间有限和隔振要求高的特点以及实际应用线谱混沌化控制技术面临的难题，通过准零刚度隔振器设计、非线性动力学分析和混沌反控制等关键技术研究，设计一套能够满足潜艇机械设备安装需求的紧凑型准零刚度隔振器，提出一套实现准零刚度隔振系统混沌反控制的方法，力求在准零刚度隔振系统中实现小振幅下的持续混沌化，从而达到低频隔振和线谱混沌化双重目的，研究成果具有重要的理论价值和工程意义。基于此思路，本项目开展和完成了如下研究工作：.1．建立了准零刚度隔振系统的一般理论模型，并开展了动力学特性研究。.（1）利用谐波平衡法和弗洛凯理论研究了单自由度准零刚度隔振系统的稳态响应及其稳定性，探究了系统参数对主共振响应的影响；.（2）推导了两自由度准零刚度隔振系统的动态特性，从激励幅值、质量比和阻尼比等方面研究了系统参数对力传递率的影响。.2．对柔性基础准零刚度隔振系统进行了局部分岔和全局性态分析。.（1）利用奇异性理论对系统在1:2内共振下的余维4分岔拓扑结构进行分析，得到了普适开折和复杂的转迁集；.（2）通过胞参考点映射法对系统全局性态进行分析，揭示了不同类型的吸引子共存规律。.3．开展了准零刚度隔振系统的线谱混沌化控制技术研究。.（1）利用双时延反馈控制实现了单自由度准零刚度隔振系统的持续混沌化；.（2）研究了基于状态反馈的广义混沌同步和基于开环加非线性闭环耦合的广义混沌同步控制策略，实现了柔性基础准零刚度隔振系统在小振幅下的持续混沌化。.4．对永磁体型准零刚度隔振器进行建模、分析、设计和试验。.（1）建立了永磁体型准零刚度隔振器的轴向磁力和刚度解析模型，并分析了系统的动力学特性；.（2）研制了永磁体型准零刚度隔振器原理样机，搭建试验台架系统并进行了隔振性能测试试验。