Stability of heated orthotropic geometrically irregular plate in a supersonic gas flow

Thin-walled geometrically irregular objects in the form of orthotropic rectangular plates are considered on the basis of the linear thermoelasticity, they are supported by the ribs symmetric with respect to middle plane. The location of the ribs coincides with the direction of the supersonic gas flow. The continuum model of the thermoelastic system “plate- ribs” was chosen. Singular differential equations of quasi-static and dynamic state of the elastic system contain tangential efforts and transverse force. Tangential efforts occur during heating of the plate. The transverse force caused by a small deflection plates is determined in the standard way via the “forcer” theory. The tangential effort is pre-determined by the solutions of singular differential equations of thermoelasticity for a geometrically irregular plate with given boundary conditions. The solution of the singular differential equations of thermoelasticity of the plate in a supersonic gas flow in quasi-static and dynamic formulation of the objectives sought in the form of sums of double trigonometric series, respectively, with the constant and variable along the time coordinate coefficients. The coefficients - approximating the function of trough - of the ranks are determined using Galerkin method as a solution of the homogeneous algebraic systems or homogeneous systems of differential equations of the second order in the case of a dynamic formulation of the problem. The solution is given in the second approximation. The critical values of the gas flow rate are determined on the basis of the standard methods of analysis of static and dynamic stability of thin-walled structures. Quantitative results are presented in tables illustrating the influence of the geometrical parameters of the “plate-ribs” thermoelastic system, the relative height of the ribs, number of ribs, the ratio of the sides of the plate, temperature, the material anisotropy on the stability of the geometrically irregular plate over the sound of the gas flow.