By the comparison between the numerical results and the linearized solution,we show some solutions of von Kármán’s equation have global feature that can becaptured by the linearized solutions, although there are some shifts in amplitudeand phase. To show the validity of this approach and polish the approximation, we use the amplitude equation approach, which can tune the amplitude and phase of the linearized solutions to make them fit. We encounter difficulty in the course of finding the amplitude equation of damping systems. To solve this problem, we propose an idea to deal with the exponential growth of the zero-th order solution. Although the phase of the approximate solution deviates from the numerical results very much, the amplitude fits well. Further investigation is under way.