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Investigation the two degree-of-freedom（DOF) wedge aeroelastic airfoil with combined freeplay and cubic nonlinearity in pitch submitted to supersonic and hypersonic flow is significant and critical for designing of the aircraft structural control surface. The classic character of the mathematic model derived from this aircraft structure is piecewise-smooth dynamics system. The Po I ncar é mapping method and Floquet theory are used for the analysis the limit cycle oscillation（LCO) flutter and chaos motion of this system. The results show that the Floquet multiplier can predict the LCO flutter and periodic-k well. It also proves that the initial condition acts important influence on the dynamics character of the airfoil. The initial condition locates in the nearby the cycle orbit can lead to the LCO and the initial condition locates nearby the saddle focus orbit can lead to chaos motion，which is the main difference from most of outcomes of airfoil flutter. The figure of the Po I ncar é also approve the results.