Aerodynamic Flutter Derivatives for a Flexible Wing with Supersonic and Subsonic Edges

A box method is developed for obtaining the generalized air forces on an oscillating flexible wing in supersonic flow with both supersonic and subsonic edges. Essentially, the method consists of representing the wing by a grid of square boxes and determining the influence of one box on another. These aerodynamic pressure influence coefficients when tabulated, permit the flutter analysis of an arbitrary wing with arbitrary normal modes to be carried out in a routine way. The coefficients satisfy the linearized unsteady supersonic flow equations and the downwash boundary conditions, and, in addition, are formulated in a manner independent of the modal shapes of the structure. The box method is applied to some simplified examples involving rigid body modes, and agreement with other methods is seen to be reasonably good. The box procedure appears to offer a simple routine manner of analyzing flexible wings for supersonic flutter analyses which is well adapted to programming on computing machinery. However, the square box method as developed here for subsonic edges is inapplicable to Mach Numbers below M = 1.414 without further modification. Some suggested modifications for extending below the M = 1.414 range are discussed in the body of the paper.