Nonlinear oscillations of a fluttering plate. II
In Part I, the title problem was studied using von Karman's large-deflect ion plate theory and quasi-steady aerodynamic theory. Here the latter theory is replaced by the full linearized (inviscid, potential flow) aerodynamic theory. Galerkin's method is used to reduce the mathematical problem to a system of nonlinear, ordinary, integral-differential equations in time, which are solved by numerical integrations. Results are presented for limit cycle deflection and frequency as functions of dynamic pressure; air/panel mass ratio; length-towidth ratio a/6; and Mach number M. 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. The numerical results obtained disclose the following. 1) Three types of oscillations are found: a) coupled-mode oscillation for M ≫ 1, b) single-mode oscillation for M ≈ 1, and c) single-mode, zero frequency oscillation (buckling) for M < 1. 2) For M = 1.414, a/6 = 0 the instability is weak, requiring a very large number of cycles to reach the limit cycle. This appears characteristic of the passage from the type a to type b oscillation listed previously. 3) As M → 1, a/6 → 0, the linear aerodynamic theory breaks down since the frequency of oscillation approaches zero and the aerodynamic forces become infinite. For M bounded away from 1 or a/6 from 0, the present analysis should be satisfactory within the limitations of inviscid potential flow. 4) 2 and 3 strongly suggest that weakness of the instability for M = 1.414, a/6 = 0, and inadequacy of linear aerodynamic theory for M → 1 and a/6 → 0 are two principal reasons for the previously observed discrepancy between theory and experiment in this regime. © 1967 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
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