Influence of Thermal Stresses on the Aeroelastic Stability of Supersonic Wings

The theory of static aeroelastic stability of supersonic wings including chordwise bending, as developed in reference 1, is further extended to include the influence of stresses arising from thermal gradients. The wing spanwise twist distribution is found to obey an ordinary differential equation of the fourth order whose coefficients depend on the thermal gradients. The influence of finite deformation is taken into account by the fact that the coefficients of the differential equation also depend on the amplitude of the deformation. The thermal stresses affect the stability in two distinct and independent ways, through its influence on the effective torsional stiffness and on the anticlastic effect. These factors act in opposite directions in such a way that if the thermal stress produces an increase in torsional stability it decreases the anticlastic stability, and vice versa. It is possible to embody the effect of the thermal stresses in a single parameter. Stability curves constitute a single family in this thermal parameter and plots are shown for three numerical values of the parameter.