基于最大耗能增效原则的惯容减震系统解析设计公式  

CLOSED-FORM DESIGN FORMULA FOR INERTER SYSTEM BASED ON THE PRINCIPLE OF MAXIMUM DAMPING ENHANCEMENT

作　　者：潘超 韩笑 张瑞甫[2,3] 逯静洲[1] PAN Chao;HAN Xiao;ZHANG Rui-fu;LU Jing-zhou(College of Civil Engineering,Yantai University,Yantai,Shandong 264005,China;State Key Laboratory of Disaster Reduction in Civil Engineering,Tongji University,Shanghai 200092,China;Department of Disaster Mitigation for Structures,Tongji University,Shanghai 200092,China)

机构地区：[1]烟台大学土木工程学院,山东烟台264005 [2]同济大学土木工程防灾国家重点实验室,上海200092 [3]同济大学结构防灾减灾工程系,上海200092

出　　处：《工程力学》2023年第4期91-101,共11页Engineering Mechanics

基　　金：山东省自然科学基金项目(ZR2018BEE03);国家自然科学基金项目(51978525,51978596);国家重点研发计划项目(2021YFE0112200);石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室开放课题项目(KF2020-13)。

摘　　要：惯容减震系统在高效吸能的同时可放大其内部耗能装置的变形,从而提高耗能减震效率,此耗能增效特性是惯容减震系统的关键机理,可作为物理意义明确的惯容系统设计原则。但目前惯容耗能增效设计方法的计算公式复杂,不便应用。为充分发挥惯容系统的耗能增效特性,提出以“最大耗能增效”为设计原则,以满足性能需求为直接导向,进而推导出解析形式的惯容减震系统设计公式。基于随机振动理论得出了单自由度惯容减震结构在白噪声激励下均方响应的解析式,并结合极值条件及零固有阻尼假定完成了惯容系统最优参数的推导。在解析公式的基础上给出了惯容减震系统基于最大耗能增效原则的设计流程,并编制相应程序进行了单自由度惯容减震结构的算例设计与验证。算例分析结果验证了该文设计原则与解析公式的正确性与有效性。An inerter system can absorb vibration energy efficiently and amplify the deformation of its internal energy dissipating device(EDD),thereby improving the EDD’s efficiency of energy dissipation and response mitigation.This is called the characteristic of damping enhancement,which is the key mechanism of the inerter system and can be used as a concise design principle for the inerter system.However,the existing damping-enhancement formulae for the design of inerter systems are complicated and inconvenient to apply.To give full play to the damping enhancement characteristic of the inerter system,the“maximum damping enhancement”is adopted as the design principle,and the satisfaction of the performance demands is taken as the direct goal.And then the closed-form design formulae are obtained.Based on the theory of random vibration,the closed-form formulae of the mean-square responses for a single-degree-of-freedom(SDOF)structure with an inerter system are obtained under the white noise excitation,and the expressions of optimal parameters of the inerter system are derived according to the extremum conditions and the non-inherent-damping assumption.The design process of the inerter damping system is provided based on the principle of damping enhancement and the closed-form formulae.The corresponding computer program is developed for the design and performance verification of SDOF structures with inerter systems.The analysis results of the design cases confirm the correctness and validity of the design principles and the simple closed-form formulae in this paper.

关 键 词：惯容系统 耗能增效 性能需求 随机响应 解析设计公式 

分 类 号：TU318[建筑科学—结构工程]