Mathematical Simulation of the Longitudinal Strain Waves Evolution in the Annular Channel with Viscous Fluid and Walls with Fractional Physical Nonlinearity

Authors: Mogilevich L.I., Popova E.V., Popova M.V. Published: 16.02.2024
Published in issue: #1(112)/2024  
DOI: 10.18698/1812-3368-2024-1-4-27

Category: Mathematics and Mechanics | Chapter: Mathematical Simulation, Numerical Methods and Software Packages  
Keywords: simulation, strain waves, annular channel, fractional nonlinearity, viscous fluid, perturbation method, generalized Shamel equation


The paper proposes mathematical model of propagation of the longitudinal nonlinear strain waves in walls of the annular channel filled with the viscous liquid of constant density, their propagation was simulated. The channel walls were considered as two infinitely long cylindrical shells with the coinciding longitudinal symmetry axes. The case was studied, where the shell material had fractional physical nonlinearity. Within the developed model framework, influence of the fluid motion inertia and its viscosity on the wave process was assessed. Asymptotic analysis of the resolving equations for the channel walls hydroelasticity was carried out using the perturbation method, and a transition was made to the two generalized Shamel equations system describing evolution of the longitudinal nonlinear strain waves in the walls of a channel under consideration. For a particular case, an exact solution of this soliton-type system was found, and it was shown that in a general case the system required numerical research. To implement the computational experiment, new difference schemes were proposed, similar to the Crank --- Nicholson scheme, to study heat propagation. The simulation showed that over time, the strain waves speed and amplitude were remaining unchanged, and the wave speed was super-sonic. When considering the exact solution as the initial condition, calculations showed coincidence between the numerical and exact solutions. This confirms adequacy of the proposed difference scheme for the generalized Shamel equations. It is shown that solitary strain waves in the channel walls are the solitons

The work was supported by the Russian Science Foundation (project no. 23-29-00140)

Please cite this article in English as: Mogilevich L.I., Popova E.V., Popova M.V. Mathematical simulation of the longitudinal strain waves evolution in the annular channel with viscous fluid and walls with fractional physical nonlinearity. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2024, no. 1 (112), pp. 4--27 (in Russ.). EDN: DCJWDO


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