Abstarct: Complex nonlinear behaviors such as chaotic motion have devastating effects on the dynamic system. In this thesis, the effect of nonlinear energy sink on vibration control of plates in supersonic flow is investigated. The system consists of a thin plate with different boundary conditions, over which a supersonic air flow is established, and is connected to a nonlinear energy sink. The aim is to improve the behavior of the system by changing the parameters and location of the non-linear energy sink. Also, the nonlinear behavior of rectangular viscoelastic plate, over which a supersonic air flow is established was examined with different boundary conditions and compared with the nonlinear elastic plate. Classical plate theory was used to obtain plate equations, and Von- Kármán strain-displacement relations were used to consider the nonlinear geometric effect. The Kelvin Voight model was also used to describe the viscoelastic properties and the “first-order piston theory" was used for supersonic aerodynamic flow. The equations of motion of the rectangular plates were extracted from the Lagrange method, and Rayleigh-Ritz discretization process. Solving the equations was done using fourth order Runge Kutta method. To investigate the dynamic behavior of the plates, the eigenvalues of the system, as well as diagrams such as Time history curves, phase portraits, Poincaré maps, and bifurcation diagrams were studied and analyzed. The results show that using nonlinear energy sinks, the behavior of the plates, which in some cases is very complex, can be changed to a simpler behavior. The effects of aspect ratio and azimuth angle were also investigated. The results show that the use of energy sink is more suitable for smaller aspect ratios, but for larger aspect ratios, viscoelastic plate performs better.