ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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MSC2010 76E99

Dynamics of viscoelastic element of flow channel

N. I. Eremeeva1, P. A. Velmisov2

AnnotationWe consider the plane problem of aerohydroelasticity on small oscillations arising during bilateral flow around a viscoelastic element located on the rectilinear wall of an infinite channel. A mathematical model describing the problem in a linear formulation and corresponding to small perturbations of homogeneous subsonic flows and small deflections of a viscoelastic element is formulated. Using the methods of the theory of functions of a complex variable, the solution of the problem is reduced to the study of the integro-differential equation with partial derivatives with respect to the deflection function of the element. To solve this equation, a numerical method based on the application of the Bubnov-Galerkin method is proposed, followed by the reduction of the resulting system of integro-differential equations to the Volterra vector equation of the second kind. On the basis of the developed numerical method the computer simulation of the dynamics of the deformable element is carried out.
KeywordsAerohydrodynamic impacts, viscoelastic element, aerohydroelasticity, integro-differential equation, Bubnov-Galerkin method, Volterra vector equation of the second kind, theory of complex variable function

1Nina I. Eremeeva, Associate Professor Department of Higher Mathematics, Dimitrovgrad Engineering and Technological Institute of the National Research Nuclear University MEPhI (294 Kuibyshev str., Dimitrovgrad, 433351, Russia), Ph.D. (Phys.-Math.), ORCID:,

2Petr A. Velmisov, Professor of the Department of Higher Mathematics, Ulyanovsk state technical University (32 North Crown str., Ulyanovsk, 432027, Russia), Dr.Sci. (Phys.-Math.), ORCID:,

Citation: N. I. Eremeeva, P. A. Velmisov, "[Dynamics of viscoelastic element of flow channel]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,21:4 (2019) 488–506 (In Russian)

DOI 10.15507/2079-6900.21.201904.488-506