基于高阶动力格式的基底隔震结构地震响应分析

Seismic Response Analysis of Base⁃isolated Buildings by the High⁃order Dynamic Procedure

隔震支座在强烈地震作用下将产生复杂的动力响应,精确掌握地震响应行为及其规律是研发高质量隔震支座和进行隔震结构设计的基础。在进行结构地震响应分析,特别是非线性分析时,采用传统逐步积分方法以及低阶格式建立起的动力时程分析方法都难以达到高精度,而采用传统高阶时间积分算法则会出现计算过程繁琐,工作量大等情况。本文采用一种基于高阶动力格式的显式时间积分新式算法,应用于基底隔震结构的地震响应分析中。首先通过自由度凝聚缩减原理,建立设置隔震支座钢筋混凝土框架结构简化计算模型;同时采用隔震支座恢复力双切线本构模型构建基底隔震体系运动方程,并转化为状态方程;进而基于微分求积(DQ)原理编制高阶动力格式算法求解状态方程;最后分析一高层基底隔震结构,在高、中、低不同频率地震波下地震响应,验证该方法适用性。结果表明,①利用静态凝聚技术建立隔震结构模型,从而构建地震响应状态方程,是高阶动力分析方法实施的基础。②结构高阶动力分析方法仅通过矩阵乘法运算即可获得结构动力响应,可较好且高效地用于解决非线性地震响应分析问题。③将结构高阶动力分析方法应用于基底隔震结构,能获得隔震结构较为精确的分析结果。

The isolation bearings will generate a complex dynamic response under strong earthquake.Accurately understanding its seismic response behavior and laws serves as the basis for developing high-quality isolation bearings and designing isolation structures.In seismic response analysis,especially in nonlinear analysis,the traditional stepwise integration method and low-order time-history analysis methods are difficult to achieve high precision.Meanwhile,the use of traditional high-order time-integration algorithm can lead to a tedious calculation process and heavy workload.This paper applies a new explicit time-integral algorithm based on a high-order dynamic scheme to the seismic response analysis of base-isolated structures.Firstly,a simplified calculation model of a reinforced concrete frame structure with isolation bearings is established based on the condensation reduction principle of degrees of freedom.Simultaneously,the motion equation of the base isolation system is constructed by using the dual tangent constitutive model of the restoring force of the isolation bearing,and converted into the state equation.Then,based on the differential quadrature(DQ)principle,a highorder dynamic scheme algorithm is developed to solve the state equation;Finally,the seismic response of a high-rise base-isolated structure under high,medium and low frequency seismic waves is analyzed to verify the applicability of this method.The results show that:①Using static condensation technology to establish the model of isolated structure,and to build the state equation of seismic response,is the basis for the implementation of high-order dynamic analysis method.②The high-order dynamic analysis method of the structure can obtain the structural dynamic response only through matrix multiplication,which can be used to solve the problem of nonlinear seismic response analysis better and efficiently.③Applying the structural high-order dynamic analysis method to the base isolated structure can yield more accurate analysis results of the isolated structure.