Simulation of strain waves evolution in the walls of coaxial annular and circular channels filled with viscous fluid and made from incompressible material with fractional physical nonlinearity

DOI: 10.34759/trd-2023-129-05

Аuthors

Bykova T. V.^*, Mogilevich L. I.^**, Evdokimova E. V.^***, Popova E. V.^****, Popova M. V.^*****

Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya str., Saratov, 410054, Russia

*e-mail: tbykova69@mail.ru
**e-mail: mogilevichli@gmail.com
***e-mail: eev2106@mail.ru
****e-mail: elizaveta.popova.97@bk.ru
*****e-mail: mari.popova.2004@internet.ru

Abstract

The article being presented develops approaches to mathematical modeling of nonlinear strain waves propagation in the continuous heterogeneous media. These models are up-to-date and scientifically significant for the prospective aerospace engineering due to the more-and-more increasing application of modern composite materials with significantly nonlinear physical and mechanical properties. The authors proposed a mathematical model for circular and annular channels completely filled with viscous fluids and formed by the two coaxial cylindrical shells. The shell material is considered incompressible and possessing the physical law with fractional degree nonlinearity, associating stresses, strains and strain intensity. Derivation of equations of the shell with fractional nonlinearity dynamics (Schamel nonlinearity) was performed to develop a model. The coupled hydroelasticity problem for the two coaxial cylindrical shells filled with viscous fluids was formulated. The fluid dynamics were considered within the framework of the Newtonian incompressible fluid model. Fluid motion in annular and circular channels is being studied as creeping one. The authors performed an asymptotic analysis of the hydroelasticity problem, and obtained a system of two nonlinear evolution equations generalizing the Schamel equation. It was demonstrated theoretically that in the considered statement, the presence of a viscous fluid in a circular channel has no effect on the nonlinear wave process in the shell-walls of the channel. The article proposes a new difference scheme for solving the obtained system of the two nonlinear equations based on application of the Grebner bases technique has been proposed. A series of computational experiments have been carried out, which revealed that the nonlinear strain waves in the walls of the considered channels are solitons.

Keywords:

mathematical modeling, nonlinear strain waves, coaxial shells, viscous fluid, fractional nonlinearity, incompressible material

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