非平稳激励下绝对位移直接求解非线性结构的时频分析  

Time-frequency analysis of nonlinear structure excitation input directly solved with absolute displacement under non-stationary excitation

作　　者：李喜梅[1,2] 陶铖 王建成 LI Ximei;TAO Cheng;WANG Jiancheng(Western Engineering Research Center of Disaster Mitigation in Civil Engineering,Lanzhou University of Technology,Lanzhou 730050,China;Institute of Earthquake Protection and Disaster Mitigation,Lanzhou University of Technology,Lanzhou 730050,China;Xinjiang Institute of Transportation Planning and Survey Design Co.,Urumqi 830002,China)

机构地区：[1]兰州理工大学西部土木工程防灾减灾教育部工程研究中心,兰州730050 [2]兰州理工大学防震减灾研究所,兰州730050 [3]新疆交通规划勘察设计研究院有限公司,乌鲁木齐830002

出　　处：《振动与冲击》2023年第9期168-176,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(52268028)。

摘　　要：强震作用下地震动能量的时-频演变特性对迟滞非线性的结构有着极大影响,然而通用有限元软件现有的计算模块进行频域分析时不能对非线性结构输入解耦的EPSD矩阵,限制了随机振动理论对大型复杂结构的仿真计算。将绝对位移直接求解的虚拟激励法引入多维多点的非线性动力方程,通过APDL的外部程序调用接口对非平稳地震动EPSD矩阵进行解耦与降维处理,并转化为独立于时间变量的四维均匀调制激励矩阵,实现对非线性结构精确高效的非平稳激励动态输入与随机动力响应的计算求解。最后以一座中承式三跨钢管混凝土系杆拱桥为例,计算拱肋、拱脚和桥面系响应的时变功率谱及方差。结果表明,绝对位移直接求解的激励输入方式很好地模拟了非线性结构体系所带来的时滞现象,为通用有限元软件实现非线性结构多维多点非平稳激励随机响应的求解与分析提供了可行性依据。Time-frequency evolution characteristics of ground motion energy under strong earthquake have a great impact on hysteretic nonlinear structures.However,when using existing calculation module of general finite element software to do frequency domain analysis,decoupled EPSD matrix can’t be input into nonlinear structures to limit simulation calculation of large and complex structures with random vibration theory.Here,the pseudo excitation method with absolute displacement to directly solve structure excitation input was introduced into multidimensional and multi-point nonlinear dynamic equations,and decoupling and dimensionality reduction were done for non-stationary ground motion EPSD matrix through APDL external program call interface,and it was converted into a four-dimensional uniformly modulated excitation matrix independent of time variables to realize accurate and efficient calculating and solving non-stationary excitation dynamic input and random dynamic responses of nonlinear structure.Finally,taking a half-through 3-span concrete-filled steel tube tied arch bridge as an example,time-varying power spectra and variances of responses of arch rib,arch foot and bridge deck system were calculated.The results showed that excitation input mode directly solved with absolute displacement can well simulate time-delay phenomenon brought by nonlinear structure system,and provide a feasible basis for solving and analyzing random responses of nonlinear structure with multi-dimensional and multi-point non-stationary excitation using general finite element software.

关 键 词：大跨桥梁 虚拟激励法 非平稳激励 绝对位移 多维多点 

分 类 号：TU352.1[建筑科学—结构工程] U441.3[建筑科学—桥梁与隧道工程]