Chaotic Motion of Two-Dimensional Viscoelastic Panel with External Excitation in Subsonic Flow

In order to study the nonlinear dynamics of a panel subjected to external excitation in subsonic flow, the nonlinear governing motion equations of a two-dimensional forced subsonic viscoelastic panel were established by Hamilton theory, and discretized to a series of ordinary differential equations using the Galerkin method. Then, the system equilibrium points and their stability were analyzed, and Melnikov's method was used to obtain the critical values of system parameters for chaos appearance. The critical relations between the external excitation amplitude, frequency, and flow velocity were discussed and compared with the results of chaotic motions by numerical simulation. The results show that the number of equilibrium points and their stability will change after the dimensionless dynamic pressure exceeds 64.42, and the critical parameters determined by Melnikov's method match up to those obtained by numerical simulation. Therefore, the proposed method can be used to judge whether the chaotic motion happens or not.