基于能量法的浮置基础减振系统解析模型  

Analytical model of floating foundation vibration reduction system based on energy method

作　　者：朱龙基 温留汉·黑沙[1,2,3] 刘彦辉 ZHU Longji;WENLIUHAN Heisha;LIU Yanhui(Earthquake Engineering Research&Test Center,Guangzhou University,Guangzhou 510405,China;Key Laboratory of Earthquake Engineering and Applied Technology in Guangdong Province,Guangzhou University,Guangzhou 510405,China;Key Laboratory of Earthquake Resistance,Earthquake Mitigation and Structural Safety,Ministry of Education,Guangzhou University,Guangzhou 510405,China)

机构地区：[1]广州大学工程抗震研究中心,广东广州510405 [2]广州大学广东省地震工程与应用技术重点实验室,广东广州510405 [3]广州大学工程抗震减震与结构安全教育部重点实验室,广东广州510405

出　　处：《地震工程与工程振动》2022年第2期104-112,共9页Earthquake Engineering and Engineering Dynamics

基　　金：国家自然科学基金项目(51778163)。

摘　　要：在设计浮置基础减振系统时,需要确定减振系统的力学参数、减振器个数及其布置形式等。虽然以有限元方法建立的实体模型比解析模型更准确,但在没有初始设计的情况下建立有限元模型所耗费的工作量过大,解析模型可以更快的获得较好的初始参数,为浮置基础减振系统的优化设计提供依据。文中基于能量法并结合Lagrange运动方程提出了由弹性构件支撑的浮置基础减振系统动力学解析模型,利用运动方程的特征分析方程推导了系统的实模态频率及复模态频率,并将所提出的模型和模态求解方法应用于量子芯片实验室的电子束曝光机浮置基础减振系统分析。对所提出的解析模型和SAP2000有限元模型进行了比较分析,结果显示文中提出的解析模型求解结果与有限元模型计算结果相对误差小于6%。解析模型的实模态计算浮置基础模态频率比复模态计算的结果更接近有限元模型的计算结果。It is necessary to determine the mechanical parameters of the vibration reduction system and the number and layout of the isolators when designing the floating foundation vibration reduction system.Although the solid model established by the finite element method is more accurate than the analytical model,the establishment of the finite element model requires excessive workload without initial design.The analytical model can easily obtain ini⁃tial parameters,which provides a basis for the optimal design of a floating foundation vibration reduction system.In this study,a dynamic analysis model of floating foundation vibration reduction system supported by elastic mem⁃bers is proposed based on the energy method and Lagrange equation of motion.The real modal frequency and com⁃plex modal frequency of the system are derived by using the characteristic analysis equation of the motion equation.The proposed analytical model is applied to the floating foundation vibration reduction system of the Electron Beam Lithography Machine in the Quantum Chip Laboratory.The proposed analytical model and SAP2000 finite element model are compared and analyzed.The results show that the relative error between the analytical model and the fi⁃nite element model is less than 6%.The modal frequency of floating foundation calculated by the real modal analy⁃sis is closer to that calculated by the finite element method than that calculated by the complex modal analysis.

关 键 词：浮置基础 空气弹簧 能量法 模态分析 精密仪器隔振 

分 类 号：TB535.1[理学—物理]