A regular variational boundary model for free vibrations of magneto-electro-elastic structures

Davi', G; Milazzo, A

doi:10.1016/j.enganabound.2010.10.004

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.

Davi', G., Milazzo, A. (2011). A regular variational boundary model for free vibrations of magneto-electro-elastic structures. ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 35, 303-312 [10.1016/j.enganabound.2010.10.004].