Shear deformable bars of doubly symmetrical cross section under nonlinear nonuniform torsional vibrations-application to torsional postbuckling configurations and primary resonance excitations

Sapountzakis, EJ; Tsipiras, VJ

dc.contributor.author	Sapountzakis, EJ	en
dc.contributor.author	Tsipiras, VJ	en
dc.date.accessioned	2014-03-01T01:34:35Z
dc.date.available	2014-03-01T01:34:35Z
dc.date.issued	2010	en
dc.identifier.issn	0924-090X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20761
dc.subject	Bar	en
dc.subject	Beam	en
dc.subject	Boundary element method	en
dc.subject	Independent warping parameter	en
dc.subject	Nonlinear vibrations	en
dc.subject	Nonuniform torsion	en
dc.subject	Primary resonance	en
dc.subject	Secondary twisting moment deformation effect	en
dc.subject	Shear deformation	en
dc.subject	Torsional postbuckling	en
dc.subject	Torsional vibrations	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Bar	en
dc.subject.other	Beam	en
dc.subject.other	Boundary elements	en
dc.subject.other	Independent warping parameter	en
dc.subject.other	Non-linear vibrations	en
dc.subject.other	Nonuniform torsion	en
dc.subject.other	Postbuckling	en
dc.subject.other	Primary resonance	en
dc.subject.other	Torsional vibration	en
dc.subject.other	Twisting moment	en
dc.subject.other	Algebra	en
dc.subject.other	Beams and girders	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Circuit resonance	en
dc.subject.other	Control nonlinearities	en
dc.subject.other	Differentiation (calculus)	en
dc.subject.other	Dynamic response	en
dc.subject.other	Elastic waves	en
dc.subject.other	Machine vibrations	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Shear deformation	en
dc.subject.other	Torsional stress	en
dc.subject.other	Boundary element method	en
dc.title	Shear deformable bars of doubly symmetrical cross section under nonlinear nonuniform torsional vibrations-application to torsional postbuckling configurations and primary resonance excitations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11071-010-9778-3	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11071-010-9778-3	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 effects of geometrical nonlinearity (finite displacement-small strain theory) and secondary twisting moment deformation. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are subjected to the most general axial and torsional (twisting and warping) boundary conditions. The resulting coupling effect between twisting and axial displacement components is also considered and a constant along the bar compressive axial load is induced so as to investigate the dynamic response at the (torsional) postbuckled state. The bar is assumed to be adequately laterally supported so that it does not exhibit any flexural or flexural-torsional behavior. A coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an independent warping parameter is formulated. The resulting equations are further combined to yield a single partial differential equation with respect to the angle of twist. The problem is numerically solved employing the Analog Equation Method (AEM), a BEM based method, leading to a system of nonlinear Differential-Algebraic Equations (DAE). The main purpose of the present contribution is twofold: (i) comparison of both the governing differential equations and the numerical results of linear or nonlinear free or forced vibrations of bars ignoring or taking into account the secondary twisting moment deformation effect (STMDE) and (ii) numerical investigation of linear or nonlinear free vibrations of bars at torsional postbuckling configurations. Numerical results are worked out to illustrate the method, demonstrate its efficiency and wherever possible its accuracy. © 2010 Springer Science+Business Media B.V.	en
heal.publisher	SPRINGER	en
heal.journalName	Nonlinear Dynamics	en
dc.identifier.doi	10.1007/s11071-010-9778-3	en
dc.identifier.isi	ISI:000283590100024	en
dc.identifier.volume	62	en
dc.identifier.issue	4	en
dc.identifier.spage	967	en
dc.identifier.epage	987	en