With the increasing complexity of aircraft’s wing structures, it becomes really important and more challenging to study the response of movable components under dynamic loads and the interactions between various components. For example, functional composite skins, used for aerodynamic sealing of the gap between the main wing surface and the movable control surface, could be separated from the control surface under the disturbances coming from ambient aerodynamic forces, and it could vibrate under the action of vortex shedding in its wake flow field. Sometimes, these complicated excitations can cause “flapping” motions between wing components, and consequently it can strongly affect the safety of the wing structure. Static contact analysis and dynamic response analysis of functional composite skin under nonlinear contact boundary conditions are conducted in this study based on FEM numerical simulations. The changes of internal stress and boundary contact force of the skin during multiple processes are studied. Further more, a simplified two-dimensional beam model is used to investigate the spatial-temporal evolutions of displacement of functional composite skin during the “flapping” process. The results show that, owing to the “flapping” effect, the displacement amplitude and boundary contact force of functional composite skin significantly increase. Compared with static contact condition, the displacement amplitude increases by about 86.25%, and the boundary contact force increases by about 20.24%. Moreover, there is a mixed effect of standing waves and traveling waves in the dynamic response of functional composite skin.