Abstract
The double linearization theory is extended to a supersonic straight cascade placed between parallel plane end walls, and the effect of spanwise-nonuniform mean loading upon the unsteady aerodynamic force for vibrating blades is studied. The three-dimensional version of the theory takes account of the unsteady spanwise aerodynamic force component due to spanwise nonuniformities of the mean blade loading and the vibration amplitude. The unsteady shock displacement effect on the unsteady aerodynamic force is found to be quasi-two-dimensional. Numerical examples are presented to demonstrate several features of the unsteady aerodynamic response ascribable to the effects of the spanwise-nonuniform angle of attack, camber and thickness of blades. The effect of nonuniformity of camber or thickness is larger than that of angle of attack. To attain a large steady loading on the stability boundary of the first mode bending vibration, it is advantageous to design blades with the angle of attack decreasing and the chamber and thickness increasing from hub to tip.
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