Regulating the vibratory motion of beams using shape optimization

Katsikadelis, JT; Tsiatas, GC

dc.contributor.author	Katsikadelis, JT	en
dc.contributor.author	Tsiatas, GC	en
dc.date.accessioned	2014-03-01T01:25:04Z
dc.date.available	2014-03-01T01:25:04Z
dc.date.issued	2006	en
dc.identifier.issn	0022-460X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17524
dc.subject	Cross Section	en
dc.subject	Differential Equation	en
dc.subject	Free Vibration	en
dc.subject	Inequality Constraint	en
dc.subject	Lower and Upper Bound	en
dc.subject	Nonlinear Optimization	en
dc.subject	Objective Function	en
dc.subject	Shape Optimization	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	Eigenvalues and eigenfunctions	en
dc.subject.other	Frequencies	en
dc.subject.other	Motion control	en
dc.subject.other	Optimization	en
dc.subject.other	Problem solving	en
dc.subject.other	Analog equation method (AEM)	en
dc.subject.other	Mass properties	en
dc.subject.other	Material volume	en
dc.subject.other	Optimization process	en
dc.subject.other	Vibrations (mechanical)	en
dc.title	Regulating the vibratory motion of beams using shape optimization	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.jsv.2005.08.002	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.jsv.2005.08.002	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	In this paper, shape optimization is used to regulate the vibrations of an Euler-Bernoulli beam having constant material volume. This is achieved by varying appropriately the beam cross-section and thus its stiffness and mass properties along its length, so that the beam vibrates with its minimum, maximum or a prescribed eigenfrequency as well as with the minimum or maximum difference between two successive eigenfrequencies. The problem is reduced to a nonlinear optimization problem under equality and inequality constraints as well as specified lower and upper bounds. The evaluation of the objective function requires the solution of the free vibration problem of a beam with variable mass and stiffness properties. This problem is solved using the analog equation method (AEM) for hyperbolic differential equations with variable coefficients. Besides its accuracy, this method overcomes the shortcoming of a FEM solution, which would require resizing of the elements and re-computation of their stiffness and mass properties during the optimization process. Certain example problems are presented, which illustrate the method and demonstrate its efficiency. (c) 2005 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.2005.08.002	en
dc.identifier.isi	ISI:000235888900017	en
dc.identifier.volume	292	en
dc.identifier.issue	1-2	en
dc.identifier.spage	390	en
dc.identifier.epage	401	en