**Papers Published**

- Dowell, E.H.,
*Nonlinear oscillations of a fluttering plate. II*, AIAA J. (USA), vol. 5 no. 10 (1967), pp. 1856 - 62 .

(last updated on 2007/04/10)**Abstract:**

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**Keywords:**

aerodynamics;elasticity;vibrating bodies;