Dynamic stability of heated geometrically irregular shallow shell of constant torsion in supersonic gas flow

G. N. Belostochny ; O. A. Myltcina

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 19 (2019) no. 4, pp. 397-408

Résumé

Heated until invariable temperature, geometrically irregular shallow shell of constant torsion blown by supersonic gas flow from one side of the main surfaces was considered. As the basis, a continual model of thermoelastic system “shell-ribs” was taken. Singular differential equations of dynamical thermostability of geometrically irregular shallow shell had summands containing “stretch-compression” and “shift\textrm” of the ribs. Tangential forces caused by heating of the shell and transversal strain were recorded by “piston theory” in a standard way. Tangential forces were preliminarily defined on the basis of the solutions of singular differential equations of momentless thermoelasticity in displacements with inhomogeneous edge conditions and were contained in a Brian form. The solution of the system of dynamical equations of thermoelasticity of the shell was searched for in the form of the sum of the double trigonometric series with time coordinate variable coefficients for bending function and polynomials for the tangential components of the field of displacement. On the basis of Galerkin procedure the system of differential equations for the coefficients of approximated series was defined. Then it was reduced to one differential equation of the forth order. The solution was obtained in the second approximation, which corresponded to two half-waves along the flow and one half-wave in perpendicular direction. Critical values of relative flow rates were defined using standard techniques of the analysis of dynamical stability of geometrically irregular shallow shell. Quantitative results were presented in the tables showing the dependence of geometrical parameters of the elastic system and temperature on the values of critical rates.