简介：ApplyingLagrange–Germain'stheoryofelasticthinplatesandHamiltonianformulation,thedynamicsofcantileverplatesandtheproblemofitsvibrationcontrolarestudied,andageneralsolutionisfinallygiven.BasedonHamiltonianandLagrangiandensityfunction,wecanobtaintheflexuralwaveequationoftheplateandtherelationshipbetweenthetransverseandthelongitudinaleigenvalues.Basedoneigenfunctionexpansion,dispersionequationsofpropagationmodeofcantileverplatesarededuced.Bysatisfyingtheboundaryconditionsofcantileverplates,thenaturalfrequenciesofthecantileverplatestructurecanbegiven.Then,analyticsolutionoftheprobleminplatestructureisobtained.Anhybridwave/modecontrolapproach,whichisbasedonbothindependentmodalspacecontrolandwavecontrolmethods,isdescribedandadoptedtoanalyzetheactivevibrationcontrolofcantileverplates.Thelow-order(controlledbymodalcontrol)andthehigh-order(controlledbywavecontrol)frequencyresponseofplatesarebothimproved.Thecontrolspilloverisavoidedandtherobustnessofthesystemisalsoimproved.Finally,simulationresultsareanalyzedanddiscussed.