Comment on "Reply by Author to A. H. Flax"

Abstract

C HOPRA, 1 in his Reply to my Comment 2 on his Note, 3 seems to have missed one of the main points of my remarks. He states that, for the special cases of supersonic panel flutter which he treated, his procedures given in Ref. 1 will lead to the same results as those indicated in Ref. 2, the two procedures being merely alternative ways of arriving at the same answer. This is not the case. In fact, Chopra's new interpretation 1 of the formulas he presented in Ref. 3 leads to a recipe which cannot be carried out at all.The transformation given in Ref. 2 relating the curve of X vs g T for a panel unrestrained by an elastic foundation to the corresponding curve for a panel restrained by an elastic foundation of stiffness, K = K^ is unique and one to one for corresponding points on the curves. The transformation depends on a knowledge not only of g T , the damping coefficient, and X, the flutter speed parameter, but also of W F , the flutter frequency. With this information, it is possible to relate points on the two curves at the same value of X by the formula 2 (D where the subscript e refers to the panel on an elastic foundation. This transformation carries point A on the flutter boundary of the unrestrained panel to the point A' of the flutter boundary of the elastically restrained panel, as shown in Fig. 1.If point A is, in fact, the flutter point of the unrestrained panel (corresponding to a given value of g r ) and if the only change in the physical parameters of the panel is the addition of the restraint of an elastic foundation, the flutter point of the restrained panel is the point B' on the transformed curve. However, there is no way to proceed directly from point A to point B'. Instead, the transformation to B' must be from point B. One cannot use Eq. (1) or any formula given by Chopra 3 to determine the value of damping corresponding to