频响函数二次正交法在Davenport风速谱下结构系列响应简明封闭解的应用研究  

Application of FRF quadratic orthogonal method in getting concise closed form solutions of structural series responses under Davenport wind speed spectrum

作　　者：葛新广 张梦丹[2] 龚景海 李创第[1,2] GE Xinguang;ZHANG Mengdan;GONG Jinghai;LI Chuangdi(School of Naval Architecture,Ocean&Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;School of Civil Engineering&Architecture,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200240 [2]广西科技大学土木建筑学院,广西柳州545006

出　　处：《振动与冲击》2021年第21期207-214,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(51468005);广西科技大学创新团队支持计划项目(校发[2016]31号);广西科技大学研究生教育创新计划项目(GKYC202010)。

摘　　要：针对Davenport风速谱激励下结构响应表达式复杂的问题,提出了结构频响函数二次正交法,并首次给出随机风振系列响应(绝对位移和层间位移)的方差和谱矩的简明封闭解。综合运用复模态法和虚拟激励法将结构的系列响应的频响函数二次正交化,并基于随机振动理论获得了结构系列响应方差、0-2阶谱矩和风振绝对加速度方差的简明封闭解。运用该方法分析一10层建筑结构的风振响应并与虚拟激励法进行对比,研究表明该方法为封闭解法且表达式简洁,并可用于验证虚拟激励法的精度。由于频响函数的二次正交化必须采用复模态法对结构体系进行解耦,故该方法也适用非经典阻尼结构基于Davenport谱的响应分析。Here,to solve the problem of complex expression of structural response under Davenport wind speed spectrum excitation,the frequency response function(FRF)quadratic orthogonal method of structures was proposed,and concise closed solutions of variances and spectral moments of structural random wind-induced series responses including absolute displacements and interlayer displacements were deduced for the first time.The complex mode method and the virtual excitation method were used to quadratically orthogonalize FRFs of structure series responses.Based on the random vibration theory,concise closed solutions for series response variances,0-2 order spectral moments and absolute acceleration variance of structural wind-induced vibration were obtained.Wind-induced vibration responses of a 10-story building structure were analyzed by using the proposed method,and the results were compared with those using the virtual excitation method.The study showed that the proposed method is a closed form solution solving method and its expression is simple,it can be used to verify the accuracy of the virtual excitation method;since the quadratic orthogonalization of FRF must use the complex mode method to decouple structure system,so this method is also suitable for response analysis of non-classical damped structures based on Davenport spectrum.

关 键 词：频响函数二次正交法 DAVENPORT谱 系列响应 谱矩 舒适度 简明封闭解 

分 类 号：TU318[建筑科学—结构工程] TU312