Nonlinear vibrations of viscoelastic plates of fractional derivative type: An AEM solution

Babouskos, NG; Katsikadelis, JT

dc.contributor.author	Babouskos, NG	en
dc.contributor.author	Katsikadelis, JT	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	18741584	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20625
dc.subject	Analog equation method	en
dc.subject	Boundary elements	en
dc.subject	Fractional partial differential equations	en
dc.subject	Fractional viscoelastic models	en
dc.subject	Nonlinear resonance	en
dc.subject	Nonlinear vibrations	en
dc.subject	Numerical solution	en
dc.subject	Plates	en
dc.subject	Viscoelasticity	en
dc.title	Nonlinear vibrations of viscoelastic plates of fractional derivative type: An AEM solution	en
heal.type	journalArticle	en
heal.identifier.primary	10.2174/1874158401004010008	en
heal.identifier.secondary	http://dx.doi.org/10.2174/1874158401004010008	en
heal.publicationDate	2010	en
heal.abstract	The nonlinear dynamic response of thin plates made of linear viscoelastic material of fractional derivative type is investigated. The resulting governing equations are three coupled nonlinear fractional partial differential equations in terms of displacements. The solution is achieved using the AEM. According to this method the original equations are converted into three uncoupled linear equations, namely a biharmonic (linear thin plate) equation for the transverse deflection and two Poisson's (linear membrane) equations for the inplane deformation under time dependent fictitious loads. The resulting thus initial value problems for the fictitious loads is a system of nonlinear fractional ordinary differential equations, which is solved using the numerical method developed recently by Katsikadelis for multi-term fractional differential equations. Several plates subjected to various loads and boundary conditions are analyzed and the influence of the viscoelastic character of the material is investigated. Without excluding other viscoelastic models, the viscoelastic material employed herein is described by the generalized Voigt model of fractional order derivative. The numerical results demonstrate the efficiency and validate the accuracy of the solution procedure. Emphasis is given to the resonance response of viscoelastic plates under harmonic excitation, where complicated phenomena, similar to those of Duffing equation occur. © Babouskos and Katsikadelis.	en
heal.journalName	Open Mechanics Journal	en
dc.identifier.doi	10.2174/1874158401004010008	en
dc.identifier.volume	4	en
dc.identifier.issue	1	en
dc.identifier.spage	8	en
dc.identifier.epage	20	en