一种含惯容及负刚度元件的隔振系统优化设计  

Optimization design of an isolation system with an inerter and an element of negative stiffness

作　　者：王锴 吴丽婷 刘飞 WANG Kai;WU Li-ting;LIU Fei(Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education),School of Internet of Things Engineering,Jiangnan University,Wuxi 214122,China)

机构地区：[1]江南大学物联网工程学院轻工过程先进控制教育部重点实验室,江苏无锡214122

出　　处：《振动工程学报》2024年第11期1836-1847,共12页Journal of Vibration Engineering

基　　金：江苏省自然科学基金资助项目(BK20211234);中国博士后科学基金资助项目(2022M711362);国家自然科学基金资助项目(61833007,62373166)。

摘　　要：通过将一类含阻尼器、弹簧、惯容的无源网络及接地的负刚度元件引入到基础隔振系统中,研究系统的优化设计问题。建立系统的动力学方程,得到无量纲化的频率响应函数。由于系统的幅频响应曲线存在四个固定点,故利用广义固定点法进行参数优化。将这四个固定点调整到同一高度,得到系统的最优惯容质量比、最优固有频率比和最优角频率比的表达式。令三个不变频率处的幅值与四个固定点处的幅值相等,计算得到最优阻尼比的表达式。通过Hurwitz稳定性判据推导得到取最优参数值时系统稳定的充分必要条件。通过与其他三种最优化隔振器进行对比,发现所提的优化后的隔振系统具有更优的H∞性能,且在多层楼房的减振中也具有更优的输出响应。This article investigates the optimization problem of a novel base isolation system by introducing a passive network consisting of one damper,one spring and one inerter and a grounded element with negative stiffness.The dynamic equations of the system are established and the frequency response function in the dimensionless form is derived.Since it is found that the amplitudefrequency response curves pass through four fixed-points,the extended fixed-point method is utilized to solve the parameter optimization problem.The explicit expressions of the optimal inertance-to-mass ratio,the optimal natural frequency ratio,and the optimal corner frequency ratio of the system are derived by adjusting the four fixed points to the same height.The expression of the optimal damping ratio is calculated by letting the amplitudes of the three invariant frequencies among the four fixed points to the same amplitudes as those of the four fixed-points.A necessary and sufficient condition for the system with optimal parameter values to be stable is derived by utilizing the Hurwitz stability criterion.Compared with other three optimal isolation systems,the optimal isolation system in this article can provide better H∞performance and better output responses in the multi-storey building vibration system.

关 键 词：基础隔振器 负刚度 惯容 广义固定点法 参数优化 

分 类 号：TU352.1[建筑科学—结构工程]