Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki (Dec 2018)
Dynamic stability of heated geometrically irregular cylindrical shell in supersonic gas flow
Abstract
On the basis of the Love model, a geometrically irregular heated cylindrical shell blown by a supersonic gas flow from one of its main surfaces is considered. The continuum model of a thermoelastic system in the form of a thin-walled shell supported by ribs along the incoming gas flow is taken as a basis. The singular system of equations for the dynamic thermal stability of a geometrically irregular shell contains terms that take into account the tension-compression and the shift of the reinforcing elements in the tangential plane, the tangential forces caused by the heating of the shell and the transverse load, as standard recorded by the piston theory. The solution of a singular system of differential equations in displacements, in the second approximation for the deflection function, is sought in the form of a double trigonometric series with time coordinate variables. Tangential forces are predefined as the solution of singular differential equations of non-moment thermoelasticity of a geometrically irregular shell taking into account boundary forces. The solution of the system of dynamic equations of thermoelasticity of the shell is sought in the form of the sum of the double trigonometric series (for the deflection function) with time coordinate variable coefficients. On the basis of the Galerkin method, a homogeneous system for the coefficients of the approximating series is obtained, which is reduced to one fourth-order differential equation. The solution is given in the second approximation, which corresponds to two half-waves in the direction of flow and one half-wave in the perpendicular direction. On the basis of standard methods of analysis of dynamic stability of thin-walled structures are determined critical values of the gas flow rate. The quantitative results are presented in the form of tables illustrating the influence of the geometrical parameters of the thermoelastic shell-edge system, temperature and damping on the stability of a geometrically irregular cylindrical shell in a supersonic gas flow.
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