Nonlinear nonuniform torsional vibrations of bars by the boundary element method

Sapountzakis, EJ; Tsipiras, VJ

dc.contributor.author	Sapountzakis, EJ	en
dc.contributor.author	Tsipiras, VJ	en
dc.date.accessioned	2014-03-01T01:33:56Z
dc.date.available	2014-03-01T01:33:56Z
dc.date.issued	2010	en
dc.identifier.issn	0022-460X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20624
dc.subject	Boundary Condition	en
dc.subject	Boundary Element Method	en
dc.subject	Cross Section	en
dc.subject	Differential Algebraic Equation	en
dc.subject	Differential Equation	en
dc.subject	Free Vibration	en
dc.subject	Generalized Eigenvalue Problem	en
dc.subject	Initial Boundary Value Problem	en
dc.subject	Model System	en
dc.subject	Numerical Solution	en
dc.subject	time discretization	en
dc.subject	Vibration Analysis	en
dc.subject.classification	Acoustics	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Analog equation methods	en
dc.subject.other	Axial displacements	en
dc.subject.other	Axial inertia	en
dc.subject.other	Coupling effect	en
dc.subject.other	Differential algebraic equations	en
dc.subject.other	Direct iteration techniques	en
dc.subject.other	Finite displacement	en
dc.subject.other	Free vibration	en
dc.subject.other	Fundamental modes	en
dc.subject.other	Generalized eigenvalue problems	en
dc.subject.other	Geometrical non-linearity	en
dc.subject.other	Governing differential equations	en
dc.subject.other	Initial-boundary value problems	en
dc.subject.other	Mass models	en
dc.subject.other	Nonlinear initial-boundary value problems	en
dc.subject.other	Nonuniform	en
dc.subject.other	Numerical solution	en
dc.subject.other	Small strains	en
dc.subject.other	Starting vectors	en
dc.subject.other	Time discretization	en
dc.subject.other	Torsional vibration	en
dc.subject.other	Torsional vibration analysis	en
dc.subject.other	Transverse displacements	en
dc.subject.other	Algebra	en
dc.subject.other	Beams and girders	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Control nonlinearities	en
dc.subject.other	Differentiation (calculus)	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Elastic waves	en
dc.subject.other	Equations of motion	en
dc.subject.other	Machine vibrations	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Vibration analysis	en
dc.subject.other	Weaving	en
dc.subject.other	Boundary element method	en
dc.title	Nonlinear nonuniform torsional vibrations of bars by the boundary element method	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jsv.2009.11.035	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jsv.2009.11.035	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section 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 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. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an ""average"" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand. © 2009 Elsevier Ltd. All rights reserved.	en
heal.publisher	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD	en
heal.journalName	Journal of Sound and Vibration	en
dc.identifier.doi	10.1016/j.jsv.2009.11.035	en
dc.identifier.isi	ISI:000274926800016	en
dc.identifier.volume	329	en
dc.identifier.issue	10	en
dc.identifier.spage	1853	en
dc.identifier.epage	1874	en