Non-linear dynamic analysis of beams with variable stiffness

Katsikadelis, JT; Tsiatas, GC

dc.contributor.author	Katsikadelis, JT	en
dc.contributor.author	Tsiatas, GC	en
dc.date.accessioned	2014-03-01T01:21:08Z
dc.date.available	2014-03-01T01:21:08Z
dc.date.issued	2004	en
dc.identifier.issn	0022-460X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16083
dc.subject	Boundary Condition	en
dc.subject	Cross Section	en
dc.subject	Differential Equation	en
dc.subject	Dynamic Equilibrium	en
dc.subject	Integral Representation	en
dc.subject	Load Distribution	en
dc.subject	Non-linear Dynamics	en
dc.subject	Time Dependent	en
dc.subject.classification	Acoustics	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Beams and girders	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Deflection (structures)	en
dc.subject.other	Differential equations	en
dc.subject.other	Stiffness	en
dc.subject.other	Analog equation method	en
dc.subject.other	Bending stiffness	en
dc.subject.other	Bernoulli-Euler beam	en
dc.subject.other	Fictitious time-dependent load distributions	en
dc.subject.other	Non-linear dynamic analysis	en
dc.subject.other	Dynamics	en
dc.title	Non-linear dynamic analysis of beams with variable stiffness	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0022-460X(03)00635-7	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0022-460X(03)00635-7	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	In this paper the analog equation method (AEM), a BEM-based method, is employed to the non-linear dynamic analysis of a Bernoulli-Euler beam with variable stiffness undergoing large deflections, under general boundary conditions which maybe non-linear. As the cross-sectional properties of the beam vary along its axis, the coefficients of the differential equations governing the dynamic equilibrium of the beam are variable. The formulation is in terms of the displacements. The governing equations are derived in both deformed and undeformed configuration and the deviations of the two approaches are studied. Using the concept of the analog equation, the two coupled non-linear hyperbolic differential equations with variable coefficients are replaced by two uncoupled linear ones pertaining to the axial and transverse deformation of a substitute beam with unit axial and bending stiffness, respectively, under fictitious time-dependent load distributions. A significant advantage of this method is that the time history of 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. Beams with constant and varying stiffness are analyzed under various boundary conditions and loadings to illustrate the merits of the method as well as its applicability, efficiency and accuracy. (C) 2003 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/S0022-460X(03)00635-7	en
dc.identifier.isi	ISI:000189216500016	en
dc.identifier.volume	270	en
dc.identifier.issue	4-5	en
dc.identifier.spage	847	en
dc.identifier.epage	863	en