Nonlinear oscillations of a fluttering plate
The problem of two-and three-dimensional plates undergoing limit cycle oscillations (subsequent to the occurrence of a linear, aeroelastic instability) has been investigated. Von Karman’s large deflection plate theory and quasi-steady aerodynamic theory have been employed. The effects of (constant) inplane load and static pressure differential have been included. Galerkin’s method has been used to reduce the mathematical problem to a system of nonlinear ordinary differential equations in time which are solved by numerical integration. Results are presented for limit cycle deflection, stress and frequency as functions of dynamic pressure, air/panel mass ratio, static pressure differential, and in-plane load and length-to-width ratio. These will be of interest in an evaluation of the fatigue life of the fluttering plate. They will also permit more detailed correlation between theory and experiment. It is determined that 1) in the range of parameters investigated, four to six modes should be used for accurate results, 2) for a buckled plate nonsimple harmonic but periodic oscillations are possible, 3) for typical plate parameters static pressure differentials as small as 10−2 psi may significantly alter the flutter boundary, and 4) the behavior of the three-dimensional plate is similar to that of the two-dimensional plate for length-to-width ratios up to two. © 1966 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
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