Shear deformation effect in flexural-torsional vibrations of beams by BEM

Sapountzakis, EJ; Dourakopoulos, JA

dc.contributor.author	Sapountzakis, EJ	en
dc.contributor.author	Dourakopoulos, JA	en
dc.date.accessioned	2014-03-01T01:31:51Z
dc.date.available	2014-03-01T01:31:51Z
dc.date.issued	2009	en
dc.identifier.issn	0001-5970	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19963
dc.subject	Boundary Condition	en
dc.subject	Boundary Element Method	en
dc.subject	Boundary Integral Equation	en
dc.subject	Boundary Value Problem	en
dc.subject	Coordinate System	en
dc.subject	Cross Section	en
dc.subject	Initial Boundary Value Problem	en
dc.subject	Integral Representation	en
dc.subject	Partial Differential Equation	en
dc.subject	Shear Deformation	en
dc.subject.classification	Mechanics	en
dc.subject.other	Beams and girders	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Boundary integral equations	en
dc.subject.other	Deformation	en
dc.subject.other	Differential equations	en
dc.subject.other	Elastic waves	en
dc.subject.other	Functions	en
dc.subject.other	Machine vibrations	en
dc.subject.other	Ordinary differential equations	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Probability density function	en
dc.subject.other	Shear deformation	en
dc.subject.other	Weaving	en
dc.subject.other	Basic equations	en
dc.subject.other	Boundary elements	en
dc.subject.other	Boundary integral equation approaches	en
dc.subject.other	Boundary values	en
dc.subject.other	Co-ordinate systems	en
dc.subject.other	Concentrated loadings	en
dc.subject.other	Coupled partial differential equations	en
dc.subject.other	Cross sections	en
dc.subject.other	Flexural-torsional vibrations	en
dc.subject.other	Free and forced vibrations	en
dc.subject.other	Initial boundary-value problems	en
dc.subject.other	Integral representations	en
dc.subject.other	Mathematical formulas	en
dc.subject.other	Nonsymmetric cross sections	en
dc.subject.other	Rotary inertias	en
dc.subject.other	Shear deformation coefficients	en
dc.subject.other	Shear deformation effects	en
dc.subject.other	Stress functions	en
dc.subject.other	Stress resultants	en
dc.subject.other	Timoshenko beams	en
dc.subject.other	Transverse displacements	en
dc.subject.other	Warping functions	en
dc.subject.other	Boundary element method	en
dc.title	Shear deformation effect in flexural-torsional vibrations of beams by BEM	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00707-008-0041-7	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00707-008-0041-7	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	In this paper, a boundary element method is developed for the general flexural-torsional vibration problem of Timoshenko beams of arbitrarily shaped cross section taking into account the effects of warping stiffness, warping and rotary inertia and shear deformation. The beam is subjected to arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting initial boundary value problem, described by three coupled partial differential equations, is solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Both free and forced vibrations are examined. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. © 2008 Springer-Verlag.	en
heal.publisher	SPRINGER WIEN	en
heal.journalName	Acta Mechanica	en
dc.identifier.doi	10.1007/s00707-008-0041-7	en
dc.identifier.isi	ISI:000263339600005	en
dc.identifier.volume	203	en
dc.identifier.issue	3-4	en
dc.identifier.spage	197	en
dc.identifier.epage	221	en