- Dowell, E.H., Nonlinear oscillations of a fluttering plate. II,
AIAA J. (USA), vol. 5 no. 10
pp. 1856 - 62 .
(last updated on 2007/04/10)
In Part I [ibid, vol. 4, 1267-75 (1966)] the problem was studied using von Karman's large-deflection plate theory and quasi-steady aerodynamic theory. Here the latter 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-to-width ratio a/b ; and Mach number M. Three types of oscillations are found: (a) coupled-mode oscillation for ≫1, (b) single-mode oscillation for M≈1, and (c) single-mode, zero frequency oscillation (buckling) for M < 1. For M=1.414, a/b=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. As M→1, a/b→ 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/b from 0, the analysis should be satisfactory within the limitations of inviscid potential flow. Strongly suggest that weakness of the instability for M=1.414, a/b=0, and inadequacy of linear aerodynamic theory for M→1 and a/b→0 are two principal reasons for the previously observed discrepancy between theory and experiment in this regime