Warping shear stresses in nonlinear nonuniform torsional vibrations of bars by BEM

Sapountzakis, EJ; Tsipiras, VJ

dc.contributor.author	Sapountzakis, EJ	en
dc.contributor.author	Tsipiras, VJ	en
dc.date.accessioned	2014-03-01T01:34:50Z
dc.date.available	2014-03-01T01:34:50Z
dc.date.issued	2010	en
dc.identifier.issn	0141-0296	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20891
dc.subject	Bar	en
dc.subject	Beam	en
dc.subject	Boundary element method	en
dc.subject	Nonlinear vibrations	en
dc.subject	Nonuniform torsion	en
dc.subject	Shear stresses	en
dc.subject	Torsional vibrations	en
dc.subject	Warping	en
dc.subject.classification	Engineering, Civil	en
dc.subject.other	Axial inertia	en
dc.subject.other	Cross section	en
dc.subject.other	Discretizations	en
dc.subject.other	Finite displacement	en
dc.subject.other	Geometrical non-linearity	en
dc.subject.other	Governing differential equations	en
dc.subject.other	Linear system of equations	en
dc.subject.other	Non-linear vibrations	en
dc.subject.other	Nonlinear initial-boundary value problems	en
dc.subject.other	Nonuniform	en
dc.subject.other	Nonuniform torsion	en
dc.subject.other	Small strains	en
dc.subject.other	Torsional vibration	en
dc.subject.other	Transverse displacements	en
dc.subject.other	Two boundary value problems	en
dc.subject.other	Variational approaches	en
dc.subject.other	Warping function	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Control nonlinearities	en
dc.subject.other	Elastic waves	en
dc.subject.other	Linear systems	en
dc.subject.other	Machine vibrations	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Ordinary differential equations	en
dc.subject.other	Shear stress	en
dc.subject.other	Strength of materials	en
dc.subject.other	Torsional stress	en
dc.subject.other	Weaving	en
dc.subject.other	Boundary element method	en
dc.subject.other	boundary condition	en
dc.subject.other	boundary element method	en
dc.subject.other	nonlinearity	en
dc.subject.other	shear stress	en
dc.subject.other	structural response	en
dc.subject.other	torsion	en
dc.subject.other	vibration	en
dc.title	Warping shear stresses in nonlinear nonuniform torsional vibrations of bars by BEM	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.engstruct.2009.12.002	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.engstruct.2009.12.002	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	In this paper a boundary element method is developed for the evaluation of warping shear stresses of bars of an arbitrary doubly symmetric constant cross section undergoing nonuniform torsional vibrations taking into account the effect of geometrical nonlinearity. The bar is Subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional and axial boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement - small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. Employing a variational approach, a coupled nonlinear initial boundary value problem with respect to the main unknown kinematical components and two boundary Value problems with respect to the primary and secondary warping functions are formulated. The solution of the last two problems is performed by a pore BEM approach requiring exclusively boundary discretization of the bar's cross section and leading to the evaluation of the warping shear stresses. The arising linear system of equations related to the secondary warping function is singular and a special technique is used to perform its regularization. The validity of the negligible axial inertia assumption is examined for the problem at hand. (C) 2009 Elsevier Ltd. All rights reserved.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	Engineering Structures	en
dc.identifier.doi	10.1016/j.engstruct.2009.12.002	en
dc.identifier.isi	ISI:000275488000012	en
dc.identifier.volume	32	en
dc.identifier.issue	3	en
dc.identifier.spage	741	en
dc.identifier.epage	752	en