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一类新的广义梁函数在多跨梁、板结构振动分析中的应用.docx

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一类新的广义梁函数在多跨梁、板结构振动分析中的应用 摘要 本文介绍了一类新的广义梁函数在多跨梁、板结构振动分析中的应用。首先，我们讨论了传统的广义梁函数及其局限性，然后提出了一类新的广义梁函数。利用这类新的广义梁函数可以方便地进行多跨梁和板的振动分析。最后，我们通过数值实验验证了这类新的广义梁函数的有效性和可行性。 关键词：广义梁函数，多跨梁，板结构，振动分析，数值实验 Introduction Theanalysisofthevibrationofmulti-spanbeamsandplatesisacomplexprobleminstructuralengineering.Inordertosimplifytheanalysisprocess,researchershaveproposedaseriesofmathematicaltools,suchasgeneralizedbeamfunctions,whichcaneffectivelyanalyzethevibrationofbeamsandplates.However,traditionalgeneralizedbeamfunctionshavelimitationsinsolvingcomplexproblems,suchasmulti-spanbeamswithdifferentboundaryconditions.Therefore,thispaperproposesanewtypeofgeneralizedbeamfunctiontosolvethesecomplexproblems. TraditionalGeneralizedBeamFunctions Traditionalgeneralizedbeamfunctionsarefunctionsthatmustsatisfythedifferentialequationsandboundaryconditionsofthebeam.Thesefunctionscanbeusedtodescribethevibrationofsingle-spanbeamswithsimpleboundaryconditions.However,formulti-spanbeamswithdifferentboundaryconditions,thereisnounifiedandefficientmethod.Moreover,traditionalgeneralizedbeamfunctionscannotusuallybeusedincomplexstructuresduetotheircomplicatedmathematicalexpressions. NewGeneralizedBeamFunctions Inordertosolvetheproblemswithtraditionalgeneralizedbeamfunctions,weproposeanewtypeofgeneralizedbeamfunction.Thenewgeneralizedbeamfunctioncanbeexpressedasapiecewisefunction,whichcombinesthefine-tunedtraditionalgeneralizedbeamfunctions.Weapplythisnewtypeofgeneralizedbeamfunctionintheanalysisofmulti-spanbeamsandplatestoshowitseffectiveness. ApplicationoftheNewGeneralizedBeamFunctions Weapplythenewgeneralizedbeamfunctionstoanalyzethevibrationofmulti-spanbeamsandplates.Firstly,wediscusstheanalysisofsingle-spanbeamsandestablishthemathematicalexpressionusingtraditionalgeneralizedbeamfunctions.Secondly,weextendthismethodtotheanalysisofmulti-spanbeams.Weestablishthemathematicalexpressionsofthenewgeneralizedbeamfunctionsthroughtheuseofpiecewisefunctionscombinedwiththefine-tuningoftraditionalgeneralizedbeamfunctions.