A regular variational boundary model for free vibrations of magneto-electro-elastic structures
- Authors: Davi', G; Milazzo, A
- Publication year: 2011
- Type: Articolo in rivista (Articolo in rivista)
- Key words: Hybrid boundaryelementmethod;Meshless methods;Free vibrations;Magnetoelasticity;Piezoelectricity
- OA Link: http://hdl.handle.net/10447/56390
Abstract
In thispaperaregularvariationalboundaryelementformulationfordynamicanalysisoftwo- dimensionalmagneto-electro-elasticdomainsispresented.Themethodisbasedonahybridvariational principleexpressedintermsofgeneralizedmagneto-electro-elasticvariables.Thedomainvariablesare approximatedbyusingasuperpositionofweightedregularfundamentalsolutionsofthestaticmagneto- electro-elasticproblem,whereastheboundaryvariablesareexpressedintermsofnodalvalues.The variationalprinciplecoupledwiththeproposeddiscretizationschemeleadstothecalculationof frequency-independentandsymmetricgeneralizedstiffnessandmassmatrices.Thegeneralizedstiffness matrixiscomputedintermsofboundaryintegralsofregularkernelsonly.Ontheotherhand,toachieve meaningfulcomputationaladvantages,thedomainintegraldefiningthegeneralizedmassmatrixis reducedtotheboundarythroughtheuseofthedualreciprocitymethod,althoughthisimpliesthelossof symmetry.Apurelyboundarymodelisthenobtainedforthecomputationofthestructuraloperators.The modelcanbedirectlyusedintostandardassemblyproceduresfortheanalysisofnon-homogeneousand layeredstructures.Additionally,theproposedapproachpresentssomefeaturesthatplaceitinthe frameworkoftheweakformmeshlessmethods.Indeed,onlyasetofscatteredpointsisactuallyneeded for thevariableinterpolation,whileaglobalbackgroundboundarymeshisonlyusedfortheintegrationof the influencecoefficients.Theresultsobtainedshowgoodagreementwiththoseavailableintheliterature provingtheeffectivenessoftheproposedapproach.