LIFT AND MOMENT COEFFICIENTS EXPANDED TO THE SEVENTH POWER OF FREQUENCY FOR OSCILLATING RECTANGULAR WINGS IN SUPERSONIC FLOW AND APPLIED TO A SPECIFIC FLUTTER PROBLEM

摘要

Linearized theory for compressible unsteady flow is used to derive the velocity potential and lift and moment coefficients in the form of power series in terms of the frequency of oscillation for a harmonically oscillating rectangular wing moving at a constant supersonic speed. Closed expressions for the velocity potential and lift and moment coef-ficients associated with pitching and translation are given to the sev-enth power of the frequency. These expressions extend the range of use-fulness of NACA Report 1028 in which similar expressions were derived to the third power of the frequency of oscillation. For example, at a Mach number of 10/9 the expansion of the potential to the third power is an accurate representation of the potential for values of the reduced frequency only up to about 0.08; whereas the expansion of the potential to the seventh power is an accurate representation for values of the reduced frequency up to about 0.2, a value of this parameter large enough to cover most rectangular-wing flutter cases likely to occur at this Mach number.nThe section and total lift and moment coefficients are discussed with the aid of several figures. In addition, flutter speeds obtained in the Mach number range from 10/9 to 10/6 for a rectangular wing of aspect ratio 4.53 by using section coefficients derived on the basis of three-dimensional flow are compared with flutter speeds for this wing obtained by using coefficients derived on the basis of two-dimensional flow.