Double linearization theory of three-dimensional cascades with vibrating blades under spanwise-nonuniform mean loading (supersonic leading-edge locus cascade)

The double linearization theory is extended to a three-dimensional straight cascade between parallel-plane end walls operating at supersonic axial velocity. Numerical examples are presented to show unsteady aerodynamic responses and flutter boundaries in correlation with cascade parameters. The three-dimensional effects are evaluated by comparing the three-dimensional theory predictions with the strip theory ones. To attain a large steady loading on the first mode bending flutter boundary, it is advantageous to design blades with angle of attack and camber decreasing from hub to tip. The three-dimensional effects are small for the lightly loaded cascades of the supersonic leading-edge locus.