A nonlinear analysis is presented for calculating the limiting amplitudes of cylindrical shell flutter using a four-mode approximation for the shell deflection. The aerodynamic pressure is approximated by linear piston theory, and the nonlinearity enters the problem through the nonlinear shallow shell equations for the cylinder. The governing equations are reduced to four modal equations by applying Galerkin's method, and limit cycle solutions are obtained by both the method of harmonic balance and by numerical integration. Two types of limit cycle flutter were obtained: (a) two-mode standing wave flutter, and (b) four-mode circumferentially traveling wave flutter. The theory indicates that the traveling wave type of flutter can occur at aerodynamic pressures below the linear flutter boundary.
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