Torsional Divergence
Lets first try to explain and interpret torsional divergence for the aerofoil structural model physically. An additional figure describing the mechanical system to discuss torsional divergence is given In steady flight the aerodynamic forces and moments, acting on the wing and trying to deform it, are balanced by the elastic restoring forces and moments. The wing does not deform from its steady position. A disturbance of the steady flight conditions introduces an additional aerodynamic moment trying to twist the wing which is resisted by the elastic moment.While the elastic moment is independent of the flight velocity, the aerodynamic moment is not. Basically, the aerodynamic moment linearly increases with the dynamic pressure. An incremental increase in twist may cause an incremental increase of the aerodynamic moment, which in turn incrementally increases the twist. Then, there may exist a critical dynamic pressure (flight velocity), when the elastic stifiness can not resist the aerodynamic moment, and the wing becomes torsionally divergent.
Lets add some mathematical expressions. The flap deflection is locked and set to zero when discussing torsional divergence. In steady flight there is assumed to be a "rigid" angle of attack α_{r}. The angle from zero lift line is then the sum of αr and an elastic twist α_{e} in the torsion spring due to aerodynamic loading:
a=a_{r}+a_{e}