待发振动与冲击悬臂论文

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1、ApplyingthePrincipleofmixedVariablesSolvetheProblemsofForcedVibrationofthecalculatingRectangularPlatebyUniformLoadChenYingjie,Fubaolian,LiGang,WuJie（YanshanUniversityQinhuangdao066004）Abstract:Inthispaper,applyingtheprincipleofmixedvariablessolvetheproblemsofforcedvibrationoftherectangularplatebyu

2、niformload,thestablesolutionofthecantileverplatesbyuniformloadcanbeworkedout.Theresultsbycalculatingnotonlyithaveacademicvalue,butalsoitcanbedirectlyreferredintheactualwork.Keywords:mixedvariables,uniformload,forcedvibration,stablesolution,cantileverplatesIntroductionRectangularthinplatesinenginee

3、ringareinawiderangeofapplications.Withthedevelopmentofeconomy,constructionofhighwaytrafficandlargeindustrialfactorybuildingandhigh-risebuildingshasdevelopedrapidly.Inthisengineering,forcedvibrationproblemofRectangularthinplatesareunavoidable.Inengineering,forcedvibrationproblemhasbecomemoreandmore

4、important.Inthepastsolution,itishardtofindasimpledisplacementfunctiontosolvetheproblemwithcomplicatedboundaryconditions.Puttingintousemixedvariablesmethodisjustneeddisplacementisweakpermitted.Inadvance,displacementneedstomeetstrain–displacementrelationsbutnottoneedtomeetdisplacementboundaryconditi

5、ons.Thismakessolvingthiskindofproblemneednotconsidercomplexdisplacementhypothesis.Accordingtotheactualbendingrectangularthinplateboundaryconditions,totalpotentialenergyofmixedvariablescanbestetteduptosolvetheproblemofforcedvibration.Thelimitationsofthemiscellaneouscalculationprocessoftheclassicals

6、olutionandcertainproblemswhicharedifficulttoresolveareovercame.Inthepaper,newmethodisprovidedtosolvetheforcedvibrationproblemwithcomplicatedboundaryconditions.Thesteady-statesolutionoftheforcedvibrationofthecantileverplatesisprovideasaexampletoproofthatmixedvariablemethodisasimpleapplicablemethodt

7、osolvetheforcedvibrationproblemofrectangularplate.BasicequationsBendingrectangularplateswithgeneralizedsupportedgesisasshowninfigure1.Totalpotentialenergyofmixedvariablesis(1)Settinguniformloadis(2)Fig.1bendingre