Abstract and Applied Analysis
Volume 2011 (2011), Article ID 975694, 32 pages
http://dx.doi.org/10.1155/2011/975694
Research Article
Thermodynamical Restrictions and Wave Propagation for a Class of
Fractional Order Viscoelastic Rods
1Faculty of Technical Sciences, Institute of Mechanics, University of Novi Sad, Trg D. Obradovića 6, 21000 Novi Sad, Serbia
2Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Serbia
3Faculty of Education, University of Novi Sad, Podgorička 4, 25000 Sombor, Serbia
4Institute of Mathematics, SANU, Kneza Mihaila 35, 11000 Belgrade, Serbia
Received 18 September 2010; Accepted 17 March 2011
Academic Editor: D. Anderson
Copyright © 2011 Teodor M. Atanacković et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We discuss thermodynamical restrictions for a linear constitutive equation containing fractional derivatives of stress and strain of different orders. Such an equation generalizes several known models. The restrictions on coefficients are derived by using entropy inequality for isothermal processes. In addition, we study waves in a rod of finite length modelled by a linear fractional constitutive equation. In particular, we examine stress relaxation and creep and compare results with the quasistatic analysis.