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This article is cited in 5 scientific papers (total in 5 papers)
Mathematical Modeling, Numerical Methods and Software Complexes
Dynamic stability of deformable elements of designs at supersonic mode of flow
P. A. Vel'misov, A. V. Ankilov Ulyanovsk State Technical University, Ulyanovsk, 432027, Russian Federation
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
The stability of deformable element of a construction in the form of a plate-strip with its flowing by supersonic flow of ideal gas is investigated. Adopted in paper definitions of stability are consistent with the concept of stability of dynamical systems by Lyapunov. For the description of dynamics of an elastic body the nonlinear mathematical model taking into account transverse and longitudinal deformations of the elastic plate is used. The model describes the associated system of partial differential equations for two unknown functions of deformations. Aerodynamic pressure upon a plate is defined according to Ilyushin's “piston” theory. On the base of the built functional for the case of hinged motionless fixing the ends of the plate the sufficient conditions of stability of the solution of the system of equations describing the length-cross oscillations of the plate are obtained. The estimation of the amplitude of deformations depending on initial conditions is made. On a specific example of one mechanical system the using of the proved theorems and estimates is shown.
Keywords:
aerohydroelasticity, mathematical modeling, dynamic stability, elastic plate, supersonic flow of gas, system of the partial differential equations, functional.
Received: December 12, 2017 Revised: February 17, 2018 Accepted: March 12, 2018 First online: March 28, 2018
Citation:
P. A. Vel'misov, A. V. Ankilov, “Dynamic stability of deformable elements of designs at supersonic mode of flow”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:1 (2018), 96–115
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https://www.mathnet.ru/eng/vsgtu1588 https://www.mathnet.ru/eng/vsgtu/v222/i1/p96
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