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1、ApplyingthePrincipleofmixedVariablesSolvetheProblemsofForcedVibrationofthecalculatingRectangularPlatebyUniformLoadChenYingjie,Fubaolian,LiGang,WuJie（YanshanUniversityQinhuangdao066004）Abstract:Inthispaper,applyingtheprincipleofmixedvariablessolvetheproblemsofforce
2、dvibrationoftherectangularplatebyuniformload,thestablesolutionofthecantileverplatesbyuniformloadcanbeworkedout.Theresultsbycalculatingnotonlyithaveacademicvalue,butalsoitcanbedirectlyreferredintheactualwork.Keywords:mixedvariables,uniformload,forcedvibration,stabl
3、esolution,cantileverplatesIntroductionRectangularthinplatesinengineeringareinawiderangeofapplications.Withthedevelopmentofeconomy,constructionofhighwaytrafficandlargeindustrialfactorybuildingandhigh-risebuildingshasdevelopedrapidly.Inthisengineering,forcedvibratio
4、nproblemofRectangularthinplatesareunavoidable.Inengineering,forcedvibrationproblemhasbecomemoreandmoreimportant.Inthepastsolution,itishardtofindasimpledisplacementfunctiontosolvetheproblemwithcomplicatedboundaryconditions.Puttingintousemixedvariablesmethodisjustne
5、eddisplacementisweakpermitted.Inadvance,displacementneedstomeetstrain–displacementrelationsbutnottoneedtomeetdisplacementboundaryconditions.Thismakessolvingthiskindofproblemneednotconsidercomplexdisplacementhypothesis.Accordingtotheactualbendingrectangularthinplat
6、eboundaryconditions,totalpotentialenergyofmixedvariablescanbestetteduptosolvetheproblemofforcedvibration.Thelimitationsofthemiscellaneouscalculationprocessoftheclassicalsolutionandcertainproblemswhicharedifficulttoresolveareovercame.Inthepaper,newmethodisprovidedt
7、osolvetheforcedvibrationproblemwithcomplicatedboundaryconditions.Thesteady-statesolutionoftheforcedvibrationofthecantileverplatesisprovideasaexampletoproofthatmixedvariablemethodisasimpleapplicablemethodtosolvetheforcedvibrationproblemofrectangularplate.Basicequat
8、ionsBendingrectangularplateswithgeneralizedsupportedgesisasshowninfigure1.Totalpotentialenergyofmixedvariablesis(1)Settinguniformloadis(2)Fig.1bendingre
