扁球面网壳在复合载荷作用下的非线性动力稳定性与混沌运动分析

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1、扁球面网壳在复合载荷作用下的非线性动力稳定性与混沌运动分析issolVedbypenuI．bationVariation．Initsfirstapproximateequations，linearnaturalf．requencyisobtained，initssecondapproxinlateequations，naturalf．requencyoftheshallowsphericalreticulatedshellisnonlinearobtained．Theproblemofthenonlineardynamicalstabilityofth

2、eshallowreticulatedsphericalshellunderstaticcombinedloadand10adofbothdynamicandstaticwasanalyzed．DuetononlineardynamicalVariationequationsandcompatibleequationsoftheshallowreticulatedconicalshell，anonlineardifferentialequationwithquadricitemswasobtainedbytheGalerkinmethodunderth

3、efixededgesboundarycondition．Inordertodiscusschaosmotion，akindofnonlineardynamicalf-reeoscillationequationwassolVed．TheproblemofstatisticattheequilibriumpointofthesystemwasdiscussedusingexponentF109uet．Accuratesolutiontothefreeoscillationequationoftheshallowreticulatedsphericals

4、hellwasobtained．ThenMelnikovf．unctionwass01ved，criticalconditionsofchaosmotionunderdifl’crentmultipleweregiVenandtheexistenceofchaosmotionwasconfirmedthroughthedigitalsimulationphaseplansandthePoincar6mapNonlineardynamicalstabilityofthisshallowsphericalreticulatedshellisanalyzed

5、bythemethodofcatastropheinchapterfive．Basedonthenonlineardynamicaltheoryofthinshells，accordingtothelargedeflectionf．undamentalequationsoftheshallowreticulatedsphericalthinshellsthenon“neardynamicalfundamentalequationsareestablishedbyusingthemodi行editerationmethodtosolVethesecond

6、aryapproximateanalyticals01utionandlookthe1argedeflectionsolutionastheinitialdenectionundertheboundaryconditionsofclampededges．DisplacementmodelisgiVenaccordingtotheboundaryconditionsofclanlpededgesandthetensionisobtainedbyusingdisplacementmodel．Theequationofthebalancedsurfaceis

7、obtainedbyusingthefirstVariationofthedynamicpotentialequaledzero．Thesystemofequationsandthesketchmapofthecorrespondingbifhrcationpointsetofthecorrespondingbalancedsurfacearegiven．Keyword：Reticulatedsphericalshells；Nonlinear；Stability；Chaosmotion；CatastropheIV兰州理工大学学位论文原创性声明和使用授权

8、说明原创性声明本人郑重声明：所呈交的论文是本人在导师的指导下独立进行研究所取得的研究成果。除了