Aeroelastic Optimization of a Panel in High Mach Number Supersonic Flow

This paper presents a solution for a least-weight skin thickness distribution for a panel with a flutter parameter constraint. This panel weighs less than any similar constant thickness panel, but has the same critical supersonic panel flutter parameter Acr. The panel rests on simple supports and is of sandwich construction. The span to chord ratio is large enough that the inertial, elastic, and aerodynamic behavior is one-dimensional. The Mach number is great enough that the aerodynamic forces acting on the upper panel surface may be accurately described by quasi-steady, linearized, supersonic aerodynamic theory. The final optimum design is obtained from theoretical and numerical methods adapted from optimal control theory. The results of this investigation show that the optimal panel thickness distribution is symmetric about the panel chord midpoint. Compared to a reference panel with constant thickness, optimum panels are found to be nearly 12 % lighter. Nomenclature a — panel chord length D(x) — panel chordwise bending stiffness m(x) = panel mass per unit area M = Mach number MR = mass ratio ; total optimum panel weight/total reference panel weight #o = aerodynamic pressure t(x) = nondimensional thickness parameter; T(x)/T0 T(x) = dimensional panel face-sheet thickness TO = dimensional reference panel face-sheet thickness, a constant W*(JC,T) = nondimensional panel displacement/chord x = nondimensional chordwise coordinate z0 = nondimensional frequency ratio parameter [Eq. (9a)] §! = reference panel ratio of face-sheet mass to total mass £ =1-* = aerodynamic parameter, critical parameter for the onset of flutter Ao = 2q0a3ID0(M2 — 1)1/2 r = time, sec o> = vibration frequency; rad/sec { } = column matrix [ ] == row matrix ()' = d()/dx