Plenary Lecture
Correctness of Fractional Derivative Models in Dynamic Problems of Viscoelastic Bodies
Professor Marina V. Shitikova
co-author: Yury A. Rossikhin
Voronezh State University of Architecture and Civil Engineering
Research Center on Dynamics of Solids and Structures
Voronezh, RUSSIA
E-mail: shitikova@vmail.ru
Abstract: The question is discussed on the possibility of utilization of such simplest fractional derivative viscoelastic models as Kelvin-Voigt and standard linear solid models for the description of the dynamic response of viscoelastic bodies, namely: beams and plates. It has been shown that the adoption of the Kelvin-Voigt model with the fractional derivative in conjunction with the time-independent Poisson’s ratio for the description of the dynamic behavior of a viscoelastic Kirchhoff-Love plate results in the fact that the given problem is reduced to the equivalent problem on dynamic response of an elastic Kirchhoff-Love plate in a viscoelastic medium with fractional damping. If one uses the fractional derivative Kelvin-Voigt model in conjunction with the time-independent coefficient of volume extension-compression for solving the same problem, what seems to be more logical from the point of view of experimental data, then such a model tunes out to be inapplicable at all. In the case of consideration of the volume relaxation for the fractional derivative Kelvin-Voigt model, its inapplicability remains, and the body of calculation is increased as this takes place. As for the fractional derivative standard linear solid model, then it remains to be correct both with and without considering the volume relaxation.
Brief Biography of the Speaker: Marina V. Shitikova is a Soros Professor and Principal Researcher at the International Center of Dynamics of Solids and Structures at Voronezh State University of Architecture and Civil Engineering in Russia. She received her MEng in Civil Engineering in 1982, a PhD degree in Structural Mechanics in 1987 from Voronezh Civil Engineering Institute, a DSc degree in Solid Mechanics in 1995 from the Institute for Problems in Mechanics, Russian Academy of Sciences and full Professorship in 1995 from Voronezh State University of Architecture and Civil Engineering. Since 1994, she has been an Associate Member of the Acoustical Society of America, since 1995 she has been a Member of the EUROMECH, GAMM, the ASME International, and Russian Association “Women in Science and Education”. She has published more than 200 papers dealing with structural mechanics, vibrations, wave dynamics, acoustics, and fractional calculus viscoelasticity. In 1998 she was awarded the Russian President's Fellowship for Outstanding Young Doctors of Sciences. She is a grantee of the International Foundation, DFG, DAAD, Fulbright Foundation, and Russian Foundation for Basic Research.