第4期丛云跃等:工程结构多刚度尺度分析与模态理论文章编号:1672-6553-2023-21(4)-023-009DOI:10.6052/1672-6553-2023-0402022-10-17收到第1稿,2023-03-18收到修改稿.*国家自然科学基金资助项目(52078399),NationalNaturalScienceFoundationofChina(52078399).†通信作者E-mail:hanrenjie@tongji.edu.cn1/2分数阶线性随机动力系统的非平稳响应解析解*孔凡1许伊键1韩仁杰2†徐军3洪旭1(1.合肥工业大学土木与水利工程学院,合肥230009)(2.同济大学土木工程学院,上海200092)(3.湖南大学土木工程学院,长沙410082)摘要提出随机激励作用下1/2分数阶线性系统非平稳响应解析解的一种新方法.首先,利用特征向量展开得到1/2分数阶阻尼系统的脉冲响应函数解析表达;之后,基于Laplace变换计算得到响应功率谱密度的解析表达式和系统均方响应.通过白噪声、调制白噪声和调制修正金井清谱三种不同随机激励类型的数值算例,利用与蒙特卡洛模拟所得结果对比证明该方法的准确性和适用性.关键词分数阶,特征向量展开,拉普拉斯变换,功率谱密度,均方响应中图分类号:O321;O324文献标志码:AAnalyticalSolutionforNon-StationaryResponseof1/2-OrderFractionalLinearStochasticDynamicalSystems*KongFan1XuYijian1HanRenjie2†XuJun3HongXu1(1.CollegeofCivilEngineering,HefeiUniversityofTechnology,Hefei230009,China)(2.CollegeofCivilEngineering,TongjiUniversity,Shanghai200092,China)(3.CollegeofCivilEngineering,HunanUniversity,Changsha410082,China)AbstractInthispaper,anovelmethodisproposedtoobtainananalyticalsolutionforthenon-stationa-ryresponseof1/2ordersystemsunderstochasticexcitation.Themethodfirstusestheeigenvectorex-pansiontoobtaintheanalyticalexpressionoftheimpulseresponsefunction.Next,ananalyticalsolutionfortheresponsepowerspectraldensityisobtainedbasedontheLaplacetransform.Throughthreeillus-trativenumericalexamples,includingsystemssubjectedtowhitenoise,modulatedwhitenoise,andmodulatedcolorednoisewithmodifiedKanai-Tajimispectrum,theresponsesofthefractionalsystemsareobtainedanalyticallyandcomparedtothepertinentMonteCarloestimatestodemonstratetheaccura-cyandapplicabilityoftheproposedmethod.Keywordsfractionalorder,eigenvectorexpansion,Laplacetransform,powerspectraldensity,meansquaredrespon...
