Authors: Atanacković, Teodor
Janev, Marko 
Konjik, Sanja
Pilipović, Stevan
Zorica, Dušan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Vibrations of an elastic rod on a viscoelastic foundation of complex fractional Kelvin–Voigt type
Journal: Meccanica
Volume: 50
Issue: 7
First page: 1679
Last page: 1692
Issue Date: 18-Jul-2015
Rank: M21
ISSN: 0025-6455
DOI: 10.1007/s11012-015-0128-x
Abstract: 
We consider vibrations of an elastic rod loaded by axial force of constant intensity and positioned on a viscoelastic foundation of complex order fractional derivative type. The solution to the problem is obtained by the separation of variables method. The critical value of axial force, guaranteeing stability, is determined.
Keywords: Dynamic stability | Elastic rod on viscoelastic foundation | Fractional order constitutive equations | Real and complex order fractional derivatives | Transversal vibrations
Publisher: Springer Link
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Integrated system for detection and estimation of fire development by real-time monitoring of critical parameters 
Development of Dialogue Systems for Serbian and Other South Slavic Languages 
Secretariat for Science of Vojvodina, Grant 114-451-1084

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