In this article, vibration and supersonic flutter analyses are studied for trapezoidal Sandwich panels. Functionally graded trapezoidal panel as well as reinforced Sandwich panel by graphene nano platelets are considered. It is assumed that the graphene platelet (GPL) nanofillers are distributed in the matrix either uniformly or non-uniformly in the direction of thickness. UD, FG-X, FG-V, FG-O and FG-A are the distribution patterns of GPLs. Based on the Kant higher-order theories, the dynamic equations of Sandwich panels reinforced with graphene nanoplates are obtained using extended Hamilton’ s principle. Dynamic pressure is estimated according to the quasi-stable theory of supersonic piston. Then, using a transformation of coordinates, the governing equations and boundary conditions are converted from the original coordinates into new computational ones. Finally, the differential squares method (DQM) to obtain the natural frequencies, the shape of the modes, and the critical aerodynamic pressure is used. The effect of different porosity distribution, porosity coefficients, distribution of graphene nanoplates, weight fraction, geometry of graphene nanofillers and geometric dimensions on natural frequencies and system instability behavior are studied.