Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIII, No. 31, pp. 7–28 (2006)
On the compressed elastic rod with rotary inertia on a viscoelastic foundation
B. Stankovic and T. M. AtanackovicDepartment of Mathematics, Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Serbia
Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia
Abstract: We study transversal vibrations of an elastic axially compressed rod on a fractional derivative type of viscoelastic foundation. We assume that the axial force has a constant and a time dependent part given by Dirac distributions. The dynamics of the system is described by a system of two partial differential equations, having integer and fractional derivatives. The solution of this system is obtained in the space of distributions and its asymptotic behavior is investigated. It is shown that the foundation increases the stability bound.
Keywords: Elastic rod, fractional derivative, viscoelasticity
Classification (MSC2000): 74H45
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Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts