A PERTURBATION METHOD FOR TREATING NONLINEAR PANEL FLUTTER PROBLEMS

The general characteristics of nonlinear panel flutter at high supersonic Mach number are examined theoretically. Von Kárman’s large deflection plate theory and quasi-steady aerodynamic theory have been employed. The effects of the structural damping have been included. Galerkin’s method has been used in the space variables and the differential system obtained is solved by an asymptotic expansion using the method of the multiple time scales. The fundamental parameter of the expansion is the increment ∈ = λ — λc of the dynamic pressure parameter λ above the critical value λc. The complete transient solution to the order of ∈5/2 is given in analytic form. The results obtained show that as a first approximation the amplitude of the limit cycle depends only upon the fundamental parameter ∈, the aspect ratio and a so-called damping parameter which takes into account the structural damping effects. The results are in excellent agreement with those obtained numerically by Do well and Kobayashi. © 1969 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.