Abstract
Elastic cylindrical shells interacting with a viscous incompressible fluid are widely used in various branches of science and technology, such as engineering and aviation engineering. They provide the possibility for solving a lot of problems, such as: reducing constructing weight and dimensions, equalizing dynamic influences and vibration level, as well as reducing friction and wearing, cooling. Mathematical model of the system, representing three coaxial cylindrical shells, freely supported at the ends, and interacting with viscous incompressible fluid between them under mechanical system harmonic vibration is constructed. This mathematical model represents a coupled system consisting of the Navier-Stokes, continuity for each fluid and equations and the ones of elastic coaxial cylindrical shells dynamics which are based on the Kirchhoff-Love hypotheses and the corresponding boundary conditions, namely: for the fluid non-flow and for free attaching for the shells. The constructed mathematical model allows to investigate the oscillations of a mechanical system consisting of coaxial elastic cylindrical shells interacting with viscous incompressible liquids in order to identify dangerous operating modes.
Highlights
Coaxial elastic thin-walled shells interacting with viscous incompressible fluid between them are of great significance for the development of modern high-tech products that are used in rocket, space and automobile industry, railway transport, agricultural machinery, fuel and energy complexes
They provide the possibility for solving a lot of problems, such as: reducing constructing weight and dimensions, equalizing dynamic influences and vibration level, as well as reducing friction and wearing, cooling
To construct a mathematical model of the mechanical system under consideration, we introduce the coordinate system O x y z associated with the base to which the mechanical system is attached, that is, the center O is located in the geometric center of the coaxial shells in the unperturbed state
Summary
Coaxial elastic thin-walled shells interacting with viscous incompressible fluid between them are of great significance for the development of modern high-tech products that are used in rocket, space and automobile industry, railway transport, agricultural machinery, fuel and energy complexes They provide the possibility for solving a lot of problems, such as: reducing constructing weight and dimensions, equalizing dynamic influences and vibration level, as well as reducing friction and wearing, cooling. The analysis of circular cylindrical shells panel flutter with ideal compressible fluid and a streamlined supersonic gas flow is carried out [13] Mathematical model of this system consisting of partial differential equations and describing viscous incompressible fluid dynamics and an elastic ribbed shell is presented in [14, 15]. We consider the construction of a mathematical model that will provide a joint consideration of the vibration of a mechanical system, the inertia of the motion of a viscous fluid, and the elasticity of three cylindrical shells of finite length freely supported at the ends of the mechanical system
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