双层准零刚度隔振系统吸引子迁移控制特性  

ATTRACTOR MIGRATION CONTROL CHARACTERISTICS OF THE TWO-STAGE QUASI-ZERO STIFFNESS VIBRATION ISOLATION SYSTEM

作　　者：马召召 余永华[1] 杨庆超[2] 周瑞平[1] 柴凯 Ma Zhaozhao;Yu Yonghua;Yang Qingchao;Zhou Ruiping;Chai Kai(School of Naval Architecture,Ocean and Energy Power Engineering,Wuhan University of Technology,Wuhan 430063,China;School of Naval Architecture and Ocean Engineering,Naval University of Engineering,Wuhan 430033,China)

机构地区：[1]武汉理工大学船海与能源动力工程学院,武汉430063 [2]海军工程大学舰船与海洋学院,武汉430033

出　　处：《力学学报》2025年第3期730-739,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(51839005,52201389);国家重点研发计划(2023YFB2503905);湖北省自然科学基金(2022CFB405);中国博士后科学基金(2024M762518)资助项目.

摘　　要：非线性隔振系统普遍存在多稳态吸引子共存现象,运行在不同吸引子上时则具有不同的隔振效果.为保证非线性隔振系统处于最优的隔振状态,以双层准零刚度隔振(two-stage quasi-zero stiffness vibration isolation,TQZS VI)系统为对象,对其吸引子迁移控制特性展开分析.首先,建立了TQZS VI系统动力学模型,采用参数延拓跟踪方法和并行胞映射方法分别揭示了TQZS VI系统全局分岔特性和吸引子共存特性,在不同激励力幅值作用下TQZS VI系统具有显著的分岔特性,包括周期运动(周期1,2和3等)以及混沌运动.然后,基于吸引子迁移控制理论,采用经典指数趋近律提出了一种基于滑模变结构的吸引子迁移控制方法,其无需建立非线性控制项且目标轨道函数传输域具备全局性.最后,采用所提出的吸引子迁移控制方法构建了TQZS VI系统迁移控制项,并揭示了TQZS VI系统在不同目标轨道以及吸引子之间的迁移控制特性.结果表明,基于滑模变结构的吸引子迁移控制方法能够有效控制TQZS VI系统的运动状态,可为非线性隔振系统状态控制和减振降噪提供一种新思路.Nonlinear vibration isolation systems commonly exhibit the coexistence of multiple stable attractors,with different vibration isolation effects when operating on different attractors.To ensure that the nonlinear vibration isolation system is in the optimal state,this study focuses on the attractor migration control characteristics of a two-stage quasizero stiffness vibration isolation(TQZS VI)system.First,the dynamic model of the TQZS VI system is established,and the global bifurcation characteristics and attractor coexistence characteristics are revealed using parameter continuation tracking methods and parallel cell mapping methods.Under different excitation force amplitudes,the TQZS VI system exhibits significant bifurcation characteristics,including periodic motion(period-1,period-2,period-3,etc.)and chaotic motion.Then,based on the theory of attractor migration control,a sliding mode variable structure-based attractor migration control method is proposed using a classical exponential approach law.This method does not require the establishment of a nonlinear control term,and the target orbit function transfer domain has globality.Finally,the migration control term for the TQZS VI system is constructed using the proposed attractor migration control method,revealing the migration control characteristics between different target orbits and attractors.The results show that the sliding mode variable structure-based attractor migration control method can effectively control the motion state of the TQZS VI system,providing a new approach for state control and noise reduction in nonlinear vibration isolation systems.

关 键 词：非线性隔振 准零刚度 吸引子 滑模变结构 迁移控制 

分 类 号：O328[理学—一般力学与力学基础]