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ID:39121436
大小:2.09 MB
页数:62页
时间:2019-06-25
《非线性地基上有限长梁的响应分析》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、摘要论文对固定简谐荷载及移动荷载作用下伯努利一欧拉梁在非线性地基上的稳态响应展开研究。系统有无穷多个自由度,其模型的运动方程为含有非线性小项的偏微分方程。首先,用多尺度法求解单自由度的杜芬振子系统的解析解。除了传统的多尺度法,文中使用了两种方法改进多尺度法:变参数法、重构法。用精确的数值解与上述各种解析解作比较,分析确定了四种振动类型(主共振、超谐波共振、亚谐波共振、不共振)最合适的解析解。然后,给出求解无穷多自由度的梁系统的解析解法和数值解法。解析解法用离散解法、直接解法互相验证后,选用前者;数值解法用了向前差分格式、中心差分格式,同样可用
2、于互相验证。再后,用具体算例分别计算梁在四种荷载(单个/两个局部同定简谐荷载、单个/N个局部移动荷载)作用下的响应,算例涵盖响应的四种振动类型。在算例的基础上分析荷载各参数与响应的关系。最后,分析结构参数对响应的影响,特别是对共振条件的影响。重载运输是中国铁路货运未来的发展方向。随着列车重量和运行密度的增加,地基的非线性效应凸显。因此,本文对非线性振动响应的基础性研究具有重要意义。关键词:非线性;偏微分方程;多尺度法;数值差分ABSTRACTThisworkisconcernedwiththesteadystateresponseofanEu
3、ler-Bemoullibeamrestingonadampednonlinearelasticfoundation,whichissubjecttOstationaryharmonicloadormovingload.Vibrationsofcontinuoussystemsarealwaysmodeledintheformofapartialdifferentialequationwithsmallnonlinearorperturbedterms.Firstly,themethodofmultiplescalesmaybeapplied
4、totheforcedsingledegreeoffreedomvibrationsystem(Duffingoscillator).Twomoresolutionsareobtainedusingamultiple—scaleapproachwithtwoproceduralstepswhichdifferfromtheusualones:varyingparameterprocedureandareconstitutionprocedure.Theseapproximateanalyticalsolutionsarecomparedwit
5、heachother,andwiththeexactnumericalresultstOanalyzetheaccuracyandapplicability(thecasesofprimaryresonance,superharmonicresonance,subharmonicresonanceandnonresonance).Secondly,themethodsofanalyticalsolutionandnumericalsolutionaregivingrespectively.Asanalyticalsolution,thedir
6、ectsolutionisusedtoverifythediscretesolution,whichischosedasthefinalanalyticalsolution.Asnumericalsolution,forwarddifferenceschemeandcentraldifferenceschemeareusedtOverifyeachother.ThiMly,numericalexamplesalepresentedtohighlighttheeffectsoftheloadparametersontheresponse,inc
7、ludingallthefourkindofvibrationtypes.Single/twoharmonicfixedlocalload,single/twomovinglocalloadareinvestigated.Finally,theimpactofstructuralparametersontheresponseisanalyzed,especiallyforresonanceconditions.HeavyhaulrailwayisaleadingdevelopmentdirectionofChinarailwayfreight
8、transportation,Thenonlineareffectcannotbeneglectedifthedisplacementofthebeamisrath
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