弱非线性系统下的耗能减震结构随机地震响应分析  

Random seismic response analysis of energy dissipation structure under weak nonlinear system

作　　者：夏雨[1] 杨盈 李锦博 余颖烨[1] XIA Yu;YANG Ying;LI Jinbo;YU Yingye(School of Civil Architecture and Engineering,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]广西科技大学土木建筑工程学院,广西柳州545006

出　　处：《广西科技大学学报》2024年第4期51-57,66,共8页Journal of Guangxi University of Science and Technology

基　　金：国家自然科学基金项目(51569005);广西自然科学基金项目(2020GXNSFAA297203,2019GXNSFBA245071);广西科技基地和人才专项(桂AD19110068,桂AD19245125)资助。

摘　　要：本文研究了结构刚度弱非线性和滞变弱非线性的耗能减震结构的随机地震响应问题。首先利用整体本构关系建立单自由度弱非线性耗能结构的运动方程;然后结合带支撑黏弹性阻尼器的等效阻尼原理和随机等效线性化法对其进行等效;最后基于FPK(Fokker-Planck-Kolmogorov)方程法推导出结构刚度弱非线性耗能结构随机地震响应值的解析解,基于等效Duffing体系法推导出结构刚度滞变弱非线性耗能结构随机地震响应值的解析解,并对这2种方法的误差进行了分析。算例分析表明:计算结果可靠、有效;相较于现有的随机等效线性化法的求解方法,FPK法和等效Duffing体系法具有更高的精度。The stochastic seismic responses of energy dissipation structures with weakly nonlinear stiffness and hysteretic weakly nonlinear stiffness are studied.The analytical solutions of these two structures are given by FPK(Fokker-Planck-Kolmogorov)equation method and equivalent Duffing system method,and the errors of both methods are analyzed.Firstly,the differential and integral equations of motion of weakly nonlinear structures with single degree of freedom including viscoelastic dampers and braces of ordinary integral model are established by using the global constitutive relation.Then,the equivalent damping principle of the supported viscoelastic damper and the stochastic equivalent linearization method are made equivalent.Finally,based on FPK equation method,the analytical solution of random seismic response value of stiffness weakly nonlinear energy dissipation system is derived.Based on the equivalent Duffing system method,the analytical solution of random seismic response value of hysteretic weakly nonlinear energy dissipation system is derived.The example shows that the calculation results are reliable and effective,and the solution accuracy based on FPK method and equivalent Duffing system method is higher than that based on the stochastic equivalent linearization method.

关 键 词：黏弹性阻尼器 随机振动 弱非线性体系 支撑 FPK方程法 随机等效线性化法 等效Duffing体系法 

分 类 号：TU318[建筑科学—结构工程]