混合隔震耗能结构基于Kanai-Tajimi谱的响应简明解析解  

Concise Analytical Solution of Response of Hybrid Isolated Energy Dissipation Structures Based on Kanai-Tajimi Spectrum

作　　者：王善库[1] 葛新广[2] 李钢[1] 赵立菊[1] WANG Shanku;GE Xinguang;LI Gang;ZHAO Liju(College of Architectural Engineering,Xinyang Vocational and Technical College,Xinyang 46400,China;School of Civil Engineering&Architecture,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]信阳职业技术学院建筑工程学院,信阳46400 [2]广西科技大学土木建筑学院,柳州545006

出　　处：《结构工程师》2020年第5期51-57,共7页Structural Engineers

摘　　要：在隔震层增加侧向黏弹性阻尼器的混合隔震耗能结构能解决传统隔震结构侧向位移较大的问题,其基于Kanai-Tajimi谱下的地震动位移、速度及谱矩分析的传统方法存在表达式复杂的窘况,提出了一种简明解析解法。首先利用达朗伯原理,获得单自由度混合隔震结构的地震动方程,并运用基于白噪声的二阶微分方程来表述Kanai-Tajimi地震动随机激励,将两者联立成运动方程组。利用复模态方法将混合隔震体系的地震动响应化为基于白噪声激励下的响应。运用白噪声激励下响应的简明特点,获得混合隔震各种响应的简明解析解,基于Wiener-Khinchin定律,得到结构响应的功率谱简明表达式,最后获得可靠度分析的3阶谱矩的简明解析解。算例表明该方法具体正确性及简明性。Hybrid isolation energy dissipation structures with lateral viscoelastic dampers on the isolationlayer can solve the problem of large lateral displacement of traditional isolation structures.A concise analyticalsolution is proposed to solve complex expressions of the traditional methods for calculating seismicdisplacement,velocity and spectral moment based on Kanai-Tajimi spectrum.Firstly,the dynamic equation of asingle-degree-of-freedom hybrid isolation structure is obtained by using the D’Alembert’s principle,and thesecond-order differential equation based on white noise is used to express the random excitation of KanaiTajimi ground motion.The two equations are combined into a set of motion equations.The response of hybridisolation system is transformed into response based on white noise excitation by complex mode method. Byusing the concise characteristics of response under white noise excitation,the concise analytical solutions ofvarious responses of hybrid isolation are obtained,which are based on Wiener-Khinchin’s law gives a conciseexpression of the power spectrum of the structural response.Finally,a concise analytical solution of the thirdorder spectral moment of the reliability analysis is obtained. Examples show that the method is correct andconcise.

关 键 词：混合隔振结构 Maxwell型黏弹性阻尼器 复模态法 谱矩 解析解 简明性 Kanai-Tajimi谱 

分 类 号：TU352.12[建筑科学—结构工程]