时滞反馈对非线性黏弹性隔振系统的竖向振动控制研究  

Vertical Vibration Control of Nonlinear Viscoelastic Isolation Systems With Time Delay Feedback

作　　者：王道航 孙博 刘春霞 周紫怡 刘羽 WANG Daohang;SUN Bo;LIU Chunxia;ZHOU Ziyi;LIU Yu(Faculty of Public Security and Emergency Management,Kunming University of Science and Technology,Kunming 650000,P.R.China;Department of Mathematics,School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming 650000,P.R.China)

机构地区：[1]昆明理工大学公共安全与应急管理学院,昆明650000 [2]云南财经大学统计与数学学院数学系,昆明650000

出　　处：《应用数学和力学》2025年第2期199-207,共9页Applied Mathematics and Mechanics

基　　金：云南省基础研究计划(青年项目)(202201AU070227)。

摘　　要：研究了时滞反馈对非线性黏弹性隔振系统的竖向振动控制情况.基于黏弹性非线性Zener模型,引入时滞控制器,建立了时滞反馈黏弹性隔振系统数学模型;采用多尺度法得到了主共振条件下的近似解析解,并根据Routh-Hurwitz理论获取了系统的稳定性条件;最后,分析了时滞参数与黏弹性隔振系统振动行为的相关性.研究结果表明,时滞控制器能够有效地对黏弹性竖向振动系统的不稳定行为和振动幅值进行控制,且时滞参数可作为独立变量调控系统振动特性.研究结果可为利用时滞控制提高黏弹性隔振系统竖向振动稳定性的应用提供理论指导.The vertical vibration control of nonlinear viscoelastic vibration isolation systems with time delay feedback was studied.Based on the viscoelastic nonlinear Zener model,a time delay controller was introduced to establish the mathematical model for time delay feedback viscoelastic vibration isolation system.The approximate analytical solution under the condition of primary resonance was obtained with the multiscale method.The stability conditions of the system were obtained based on the Routh-Hurwitz theory.Finally,the correlation between the time delay parameters and the vibration behavior of the viscoelastic vibration isolation system was analyzed.The results show that,the time delay controller can effectively control the unstable behaviors and vibration amplitudes of the viscoelastic vertical vibration system,and the time delay parameters can be used as independent variables to regulate the vibration characteristics of the system.The work provides a theoretical guidance for the application of time delay control to improve the vertical vibration stability of viscoelastic vibration isolation systems.

关 键 词：黏弹性隔振器 非线性振动 时滞反馈控制 Zener模型 多尺度法 稳定性 

分 类 号：O322[理学—一般力学与力学基础]