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1、ApplyingthePrincipleofmixedVariablesSolvetheProblemsofForcedVibrationofthecalculatingRectangularPlatebyUniformLoadChenYingjie,Fubaolian,LiGang,WuJie（YanshanUniversityQinhuangdao066004）Abstract:Inthispaper,applyingtheprincipleofmixedvariablessolvetheproblemsofforcedvibrationofthere
2、ctangularplatebyuniformload,thestablesolutionofthecantileverplatesbyuniformloadcanbeworkedout.Theresultsbycalculatingnotonlyithaveacademicvalue,butalsoitcanbedirectlyreferredintheactualwork.Keywords:mixedvariables,uniformload,forcedvibration,stablesolution,cantileverplatesIntroduc
3、tionRectangularthinplatesinengineeringareinawiderangeofapplications.Withthedevelopmentofeconomy,constructionofhighwaytrafficandlargeindustrialfactorybuildingandhigh-risebuildingshasdevelopedrapidly.Inthisengineering,forcedvibrationproblemofRectangularthinplatesareunavoidable.Ineng
4、ineering,forcedvibrationproblemhasbecomemoreandmoreimportant.Inthepastsolution,itishardtofindasimpledisplacementfunctiontosolvetheproblemwithcomplicatedboundaryconditions.Puttingintousemixedvariablesmethodisjustneeddisplacementisweakpermitted.Inadvance,displacementneedstomeetstrai
5、n–displacementrelationsbutnottoneedtomeetdisplacementboundaryconditions.Thismakessolvingthiskindofproblemneednotconsidercomplexdisplacementhypothesis.Accordingtotheactualbendingrectangularthinplateboundaryconditions,totalpotentialenergyofmixedvariablescanbestetteduptosolvetheprobl
6、emofforcedvibration.Thelimitationsofthemiscellaneouscalculationprocessoftheclassicalsolutionandcertainproblemswhicharedifficulttoresolveareovercame.Inthepaper,newmethodisprovidedtosolvetheforcedvibrationproblemwithcomplicatedboundaryconditions.Thesteady-statesolutionoftheforcedvib
7、rationofthecantileverplatesisprovideasaexampletoproofthatmixedvariablemethodisasimpleapplicablemethodtosolvetheforcedvibrationproblemofrectangularplate.BasicequationsBendingrectangularplateswithgeneralizedsupportedgesisasshowninfigure1.Totalpotentialenergyofmixedvariablesis(1)Sett
8、inguniformloadis(2)Fig.1bendingre
