Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Mathematical and сomputer modeling of nonlinear waves dynamics in a coaxial physically nonlinear shells with viscous incompressible fluid between them

This study focuses on the analysis of nonlinear wave propagation deformations in the elastic physically nonlinear coaxial cylindrical shells containing a viscous incompressible fluid between them. Wave processes in an elastic cylindrical shell without interacting with fluid were previously studied from the standpoint of the theory of solitons. The presence of fluid required developing a new mathematical model and computer modeling of processes occurring in the system. 

Nonlinear Deformation Waves in a Geometrically and Physically Nonlinear Viscoelastic Cylindrical Shell Containing Viscous Incompressible Fluid and Surrounded by an Elastic Medium

The present study is devoted to analysis of nonlinear deformation of longitudinal waves in a cylindrical shell surrounded by an elastic medium and containing viscous incompressible fluid inside. The physical properties of the shell are defined by the equations of quadratic theory of viscoelasticity, which takes into account the linear elastic volume strain.

Wave Occurrences Mathematical Modeling in Two Geometrically Nonlinear Elastic Coaxial Cylindrical Shells, Containing Viscous Incompressible Liquid

The investigation of deformation waves behavior in elastic shells is one of the important trends in the contemporary wave dynamics. There exist mathematical models of wave motions in infinitely long geometrically non-linear shells, containing viscous incompressible liquid, based on the related hydroelasticity problems, which are derived by the shell dynamics and viscous incompressible liquid equations in the form of generalized Korteweg – de Vries equations.

Nonlinear Waves Mathematical Modeling in Coaxial Shells Filled with Viscous Liquid

There exist wave motion mathematical models in infinitely long geometrically nonlinear shells filled with viscous incompressible liquid. They are based on related hydroelasticity problems, described by dynamics and viscous incompressible liquid equations in the form of generalized KdV equations. Mathematical models of wave process in infinitely long geometrically nonlinear coaxial cylindrical shells are obtained by means of the small parameter perturbation method.