滞后阻尼体系地震反应的中心差分虚初始条件法  

A CENTRAL DIFFERENCE VIRTUAL INITIAL CONDITION METHOD FOR SEISMIC RESPONSE ANALYSIS OF SYSTEMS WITH HYSTERETIC DAMPING

作　　者：祁文睿 潘旦光[1,2] 高永涛[1] 付相球 QI Wen-rui;PAN Dan-guang;GAO Yong-tao;FU Xiang-qiu(Civil and Resource Engineering School,University of Science and Technology Beijing,Beijing 100083,China;Beijing Key Laboratory of Urban Underground Space Engineering,University of Science and Technology Beijing,Beijing,100083,China)

机构地区：[1]北京科技大学土木与资源工程学院,北京100083 [2]城市地下空间工程北京市重点实验室,土木与资源工程学院,北京科技大学,北京100083

出　　处：《工程力学》2020年第9期94-102,共9页Engineering Mechanics

基　　金：土木工程防灾国家重点实验室开放基金项目(SLDRCE15-01)。

摘　　要：针对滞后阻尼体系的直接积分法解发散问题,提出了中心差分虚初始条件法。该方法以实数初始条件为基础,建立相应的虚初始条件,以消除自由振动中的发散项,而使直接积分法的计算结果收敛到稳定解;并以有条件稳定的中心差分数值计算方法为基础,建立中心差分虚初始条件法的直接积分程序;对三个不同自振频率体系在三条地震波作用下进行中心差分虚初始条件法、解析解和频域解的数值计算。计算结果表明:频域分析结果仅包含稳态解,这将导致低自振频率体系在振动的初始阶段将产生显著误差;中心差分虚初始条件法对不同工况的计算结果都是稳定的,且收敛到包括瞬态反应的解析解。A central difference virtual initial condition method is proposed to address the instability of the solution of hysteretic damping system.The proposed method develops virtual initial conditions associated with the real initial conditions,which generates the direct integration solution eliminating the divergence term of complementary solution and converges to the exact solution.Then,the procedure of central difference virtual initial condition method is established based on central difference method which is of conditional stability.Numerical examples of three different natural frequency systems under three different seismic excitations are analyzed by the central difference virtual initial condition method,the analytical solution and the frequency domain method,respectively.The results show that the frequency domain analysis results only contain the steady state solutions,which will lead to significant errors in the initial stage of vibration of low natural frequency system;the central differential virtual initial condition method is stable for different conditions,and it will converge to theoretical solution including transient response.

关 键 词：滞后阻尼 中心差分法 地震反应 发散 初始条件 

分 类 号：O342[理学—固体力学]