ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Mogilevich L. I., Popova E. V. Longitudinal waves in the walls of an annular channel filled with liquid and made of a material with fractional nonlinearity. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 3, pp. 365-376. DOI: 10.18500/0869-6632-003040, EDN: RKTVVT

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Language: 
English
Heading: 
Nonlinear Waves. Solitons. Autowaves. Self-Organization.
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003040
EDN: 
RKTVVT

Longitudinal waves in the walls of an annular channel filled with liquid and made of a material with fractional nonlinearity

Autors: 
Mogilevich Lev Ilyich, Yuri Gagarin State Technical University of Saratov
Popova Elizaveta Viсtorovna, Yuri Gagarin State Technical University of Saratov
Abstract: 

Purpose of this paper is to study the evolution of longitudinal strain waves in the walls of an annular channel filled with a viscous incompressible fluid. The walls of the channel were represented as coaxial shells with fractional physical nonlinearity. The viscosity of the fluid and its influence on the wave process was taken into account within the study.

Metods. The system of two evolutionary equations, which are generalized Schamel equations, was obtained by the two-scale asymptotic expansion method. The fractional nonlinearity of the channel wall material leads to the necessity to use a computational experiment to study the wave dynamics in them. The computational experiment was conducted based on obtaining new difference schemes for the governing equations. These schemes are analogous to the Crank–Nicholson scheme for modeling heat propagation.

Results. Numerical simulation showed that over time, the velocity and amplitude of the deformation waves remain unchanged, and the wave propagation direction concurs with the positive direction of the longitudinal axis. The latter specifies that the velocity of the waves is supersonic. For a particular case, the coincidence of the computational experiment with the exact solution is shown. This substantiates the adequacy of the proposed difference scheme for the generalized Schamel equations. In addition, it was shown that solitary deformation waves in the channel walls are solitons.

Key words: 
Wave dynamics
Annular channel
Viscous fluid
Fractional nonlinearity
Computational experiment
Acknowledgments: 
The study was funded by Russian Science Foundation (RSF) according to the project No. 23-29-00140.
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Received: 
26.02.2023
Accepted: 
14.03.2023
Available online: 
11.05.2023
Published: 
31.05.2023
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