含负刚度的调谐惯容质量减振系统的参数优化解析及设计公式  

Analytical parametric optimization analysis and design formulas of tuned inerter mass vibration control system with negative stiffness

作　　者：苏宁 陈昭庆[1] 边菁 曾聪[1] SU Ning;CHEN Zhaoqing;BIAN Jing;ZENG Cong(School of Civil Engineering and Architecture,Northeast Electric Power University,Jilin 132012,China;Tianjin Research Institute for Water Transport Engineering,Ministry of Transport,Tianjin 300456,China;School of Civil Engineering,Chongqing University,Chongqing 400045,China)

机构地区：[1]东北电力大学建筑工程学院,吉林吉林132012 [2]交通运输部天津水运工程科学研究所,天津300456 [3]重庆大学土木工程学院,重庆400045

出　　处：《振动工程学报》2025年第4期803-815,共13页Journal of Vibration Engineering

基　　金：国家重点研发计划项目(2022YFB2602302);国家自然科学基金资助项目(52202415);山西省基础研究计划项目(202203021221044);中央级公益性科研院所基本科研业务费专项(TKS20230201)。

摘　　要：惯容器和负刚度装置能够提高减振器的耗能性能,被越来越多地融入新型高性能减振装置中。本文对含负刚度的调谐惯容质量减振系统(NS⁃TIMS)进行了参数优化解析研究。建立了NS⁃TIMS在不同安装位置、应用场景(层间吸振、基底隔振)、激励类型下的运动方程及传递函数统一模型。在定点理论的基础上,得到了综合考虑H∞和H2范数的NS⁃TIMS最优参数解析解。考虑典型的应用条件,对优化参数解析公式进行分析和简化,得到了一种基于“等效惯质比”的NS⁃TIMS参数设计公式,并讨论了设计公式的适用条件。风振控制和基础隔振实际算例分析验证了考虑实际结构阻尼比和随机荷载频谱特性条件下的设计公式的有效性。同时发现NS⁃TIMS在高柔结构吸振和辅助基础隔振方面均具有优越的性能。Inerters and negative stiffness devices can improve the energy dissipation performance of vibration absorbers.An increasing number of applications of them in novel high-performance vibration suppression have been witnessed.In this paper,analytical parametric optimization analyses on the tuned inerter mass systems with negative stiffness(NS-TIMS)are performed.A unified model of governing equations and transfer functions for NS-TIMS under different installation locations,application scenarios(such as inter-layer vibration absorption,and base isolation)and excitation types is established.Based on the fixed-point theory,the optimal parameters of NS-TIMS considering both H∞and H2 norms are analytically derived.Considering typical application conditions,the analytical formulas are further analyzed and simplified.Consequently,the design formulas for the optimal parameters of NS-TIMS based on the“equivalent inertial mass ratio”are proposed.The application scopes of the design formula are discussed.Through numerical cases on the practical examples of wind-induced vibration control and seismic base isolation,the effectiveness of the design formulas considering the actual structural damping ratio and spectral characteristics of stochastic excitations is verified.It is also revealed that NS-TIMSs have superior performances in both high flexible structure vibration absorption and auxiliary base vibration isolation.

关 键 词：基础隔振 动力吸振器 负刚度 惯容 H∞优化 

分 类 号：TU352.1[建筑科学—结构工程]