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 Wysłany: Sob 23:46, 07 Maj 2011 Temat postu: ed hardy bikinit Piezoelectric Mixed Variational P |
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Piezoelectric Mixed Variational Principle and Free Vibration Analysis of Laminated Plates
ionforelasticbodiesandshellsofrevolution. JournalofAppliedMechanics, l992; 59:587-595l1 Tang Limin , et al. Mixed state Hamiltonian element of the semi-analytical solution and the laminated plate calculations. Computational Structural Mechanics and Applications , 1992; 9 (4) :347-36O12FanJR, YeJQ. Aseriessolutionoftheexactequationforthickorthotropicplates. InternationalJournalofSolidsandStructures, 1990; 26 (7) :773-778ModifiedMixedVariationalPrincipleforPiezoelectricMaterialsandFreeVibrationAnalysisofLaminatedPlatesQingGuanghuiQiuJiajunTaNa (MechanicsDepartmentofSchoolofMechanicalEngineering,jordan shoes, TianjinUniversity,abercrombie uk, Tianjin, 300072,franklin and marshall sale, China) Abstract: ModifiedHellinger-Reissner (H-R) mixedvariationalprincipleforthefreevibrationproblemofthree-dimensionalpiezoelectricmaterialwithmechanical-electriccouplingeffectisestablished; theHamiltoncanonicalequationofthere-dimen-sionalpiezoelectricbodiesisderivedfromthevariationalprinciple, namely, thecontroldifferentialequationforfreevibrationofpiezoelectricmateria1. Basedonthematrixtheory, withoutanyassumptionaboutdisplacementsandstressesmodel, theexactsolutionoffreevibrationofthelaminatedpiezoelectricrectangularplateswithsimplesupportispresented. Numericalexampleshowsthatthelownaturalfrequenciesofdirectandinversepiezoelectriceffectareingoodagreementwiththoseofpublishedreference. Thevariationalprincipleestablishedinthispaperbenefitstoderivethefiniteelementmethodorsemi-analyticalsolutionforpiezoelectricmaterialdynamicsproblem. Keywords: elasticvibration; piezoelectricmaterial; Hamiltoncanonicalequation; modifiedH-Rmixedvariationalprinciple first author : Qing brilliant ,ed hardy bikinit, male, post-doctoral ,mbt shoes sale, 1968 l1 months 17El students. Phone : (022) 27401727; E-mail: qingluke @ 126. com
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