ralrigidityat,Y=,andDbistheflexuralrigidityatY=b.Inthis‘case,Eq.()canbereducedtoSolutionTherectangularplateisassumedtobesimplysupportedalongtwooppositeedgesparalleltotheY-direction.Tosolvethegoverningequationwiththeprescribedboundaryconditions,ageneralizedLevy-typeapproachisemployedaswhereYm(y)isanunknownfunctiontobedetermined.SubstitutingEq.()intoEq.()yieldsthefollowingdifferentialequation:第页Thesolutionoftheaboveequationconsistsoftwoparts,i.e,thegeneralsolutionYmoofthehomogeneousdifferentialequationandtheparticularsolutionYmoofthenohomogeneousdifferentialequation.Thus,thesolutionofEq.()canbeexpressedas..Generalsolutionofgoverningequation()TofindthesolutionofEq.(),wefirstconsiderthefollowingfourth-orderhomogeneousdifferentialequationwithvariablecoefficients:TheaboveequationcanbetransformedintoaWhittakerequation,andthesolutioncanbeexpresMathematicalModeling,,-()[]Jodaei,A.,Jalal,M.,andYes,M.H.Free