Some important advantages of composite materials such as their high weight to strength ratio, was the cause of their prevalent use in many industrial cases in past decades. Corrugated panels are special kinds of composite structures that their ability to withstand loads in one direction and be flexible in other direction has made them suitable for morphing structures. The principal application of this type of composite structures is in the morphing airfoils where they are subjected to the aerodynamic loading in various flow regimes. Since many researches on the static and dynamic behavior of such interesting structures were reported in the literature, having a comprehensive insight into their aeroelastic behavior is of crucial importance. Considerable amounts of researches were done that focused on static and dynamic behavior of these special composite panels; subsequently, the main goal of the present study is to determine time response into arerodynamic loading and stability analysis of corrugated composite panels. An equivalent analytical model to characterize the trapezoidal corrugated core is presented. A complete set of analytical formulas was derived based on energy approach for elastic modulus in different directions, transverse and in-plane shear modulus, in-plane Poisson’s ratio and mass density of the equivalent model. The proposed approach is general and able to model different corrugation geometry parameters, overcoming the main limitation of the existing analytical formulations. To validate the precision and accuracy of the derived formulation, obtained results were compared with the reported results in literature as well as the finite element simulations. Afterwards, using the proposed model in conjunction with Hamilton principle and considering first order quasi-steady aerodynamic theory (linearized piston theory) as a simple and suitable method for aerodynamic loading in supersonic flow regime, time responses of the panel, FFT and phase diagrams of were obtained. Then an aeroelastic finite element model were provided in ABAQUS (an FEM package) to evaluate the validity of the results obtained by Galerkin. In this FE model the panel was modeled as a shear deformable composite shell considering the effect of large out-of-plane displacements due to its nonlinear geometry. Considering the fact that ABAQUS dose not have the capability to apply a kind of loading that is dependent to time and spatial derivatives of out-of-plane translational DoF (linearized piston theory) as a typical loading, a DLOAD FORTRAN subroutine were provided to apply the aerodynamic loading.The results of these analysis showed that the motion of the panel would be eather simple harmonic or non-harmonic but periodic limit cycle oscillations. A comparison between Galerkin approach and FEM results were made and acceptable agreement were demonstrated. Furthermore, the effects of shape memory alloys on vibration of corrugated panels were also studied. Keywords : Corrugated composite structures, Finite element method, Limit cycle oscillations, Linerized piston theory, Morphing airfoils, Shape memory alloy, Homogenization technique and Supersonic flow regime