About the Aerothermoelastic Stability of Panels in Supersonic Flows

Abstract

This article provides new insights into the aerothermoelastic stability of thin plates. Particularly, the issue of loss of stability of an isotropic plate-strip of constant thickness immersed in a supersonic flow field and subjected to a variable temperature field through the thickness is examined. Using the basic principles of the theory of aerothermoelasticity of isotropic bodies, the theories of flexible panels, and the linear law of temperature field through the thickness of the panel, the stability equations and associated boundary conditions are obtained. As expected, the coefficients of the aerothermoelastic governing equations depend on the thermal load, and consequently the panel-flutter critical speed depends on temperature. The model takes into account quadratic and cubic aerodynamic non-linearities as well as cubic geometric non-linearities. Due to the inhomogeneity of the temperature field distribution across the thickness plate buckling instability occurs. This instability accounts for the deformed shape of the plate and the stability boundary depends on the variables characterizing the flow speed, the temperature of the middle plane and the temperature gradient in the direction normal to the plane. It is shown that the combined effect of the temperature field and free-stream regulates the process of stability and the temperature field can significantly change the flutter critical speed and flutter behavior. The problem of stability is also considered in the non-linear framework. The existence and behavior of flutter-type vibrations is investigated at pre- and post-critical speeds. The influence of the temperature field on the dependency of the limit cycle amplitude as a function of speed is studied. Results and discussions are presented along with pertinent concluding remarks.