 Posted: Sat 23:52, 07 May 2011 Post subject: alexa mulberry taske Piezoelectric Mixed Variation |
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Piezoelectric Mixed Variational Principle and Free Vibration Analysis of Laminated Plates ionforelasticbodiesandshellsofrevolution. JournalofAppliedMechanics, l992; 59:587-595l1 Tang Limin ,mbt shoes sale, 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, TianjinUniversity, Tianjin, 300072, China) Abstract: ModifiedHellinger-Reissner (H-R) mixedvariationalprincipleforthefreevibrationproblemofthree-dimensionalpiezoelectricmaterialwithmechanical-electriccouplingeffectisestablished; theHamiltoncanonicalequationofthere-dimen-sionalpiezoelectricbodiesisderivedfromthevariationalprinciple, namely,Franklin Marshall pas cher, thecontroldifferentialequationforfreevibrationofpiezoelectricmateria1. Basedonthematrixtheory, withoutanyassumptionaboutdisplacementsandstressesmodel, theexactsolutionoffreevibrationofthelaminatedpiezoelectricrectangularplateswithsimplesupportispresented. Numericalexampleshowsthatthelownaturalfrequenciesofdirectandinversepiezoelectriceffectareingoodagreementwiththoseofpublishedreference. Thevariationalprincipleestablishedinthispaperbenefitstoderivethefiniteelementmethodorsemi-analyticalsolutionforpiezoelectricmaterialdynamicsproblem. Keywords: elasticvibration; piezoelectricmaterial; Hamiltoncanonicalequation; modifiedH-Rmixedvariationalprinciple first author : Qing brilliant ,abercrombie günstig, male, post-doctoral ,alexa mulberry taske, 1968 l1 months 17El students. Phone : (022) 27401727; E-mail: qingluke @ 126. com 相关的主题文章： alexa mulberry taske Indian iron enterprise site m Christian Louboutin Screen Printing Printing Stand abercrombie milano Desktop microprocessor to the a |
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