摘要
TheseparationofvariablesisemployedtosolveHamiltoniandualformofeigenvalueproblemfortransversefreevibrationsofthinplates,andformulationofthenaturalmodeinclosedformisperformed.Theclosed-formnatu-ralmodesatisfiesthegoverningequationoftheeigenvalueproblemofthinplateexactlyandisapplicableforanytypesofboundaryconditions.Withallcombinationsofsimply-supported(S)andclamped(C)boundaryconditionsappliedtothenaturalmode,themodeshapesareobtaineduniquelyandtwoeigenvalueequationsarederivedwithrespecttotwospatialcoordinates,withtheaidofwhichthenormalmodesandfrequenciesaresolvedexactly.ItwasbelievedthattheexacteigensolutionsforcasesSSCC,SCCCandCCCCwereunabletobeobtained,however,theyaresuccessfullyfoundinthispaper.ComparisonsbetweenthepresentresultsandtheFEMresultsvalidatethepresentexactsolutions,whichcanthusbetakenasthebenchmarkforverifyingdifferentapproximateapproaches.
出版日期
2009年02月12日（中国Betway体育网页登陆平台首次上网日期，不代表论文的发表时间）
