Laboratory studies show that the mechanical properties and behavior of nano-structures are different from other materials. The discovery of stable families of carbon nano-structures, such as graphene sheets (GSs), fullerenes, carbon nano-tubes (CNTs), etc. has created a profound impact on nano-science and nanotechnology. These nano-structured materials are basic building blocks of nanotechnology with broad potential applications in the emerging ?eld of nano electromechanical systems (NEMS). Theoretical analyses of nanostructures are becoming increasingly important due to dif?culties encountered in experiments as the size of physical systems is scaled down into the nanometer scale. Of these theoretical analyses, atomistic simulations are limited to very small length and time scales due to being computationally expensive. Thus, the notions of continuum mechanics have attracted a great deal of attention of many researchers to treat structures at the nano-scale. The vibrational response of nano-structures is of great technical importance in nanotechnology theoretically. The vibrational response of a nano-plate, subject to dynamic forces resulting from a fluid flow is considered in this research, and the nano-plate is transformed into a pressurized channel by adding two rigid walls and a roof. Moreover, the corresponding critical velocities are obtained resulting from static and dynamic instabilities. Narvier-Stokes’ equation is used for modeling the effect of fluid on the plate. Furthermore, Bernolli’s equation for the fluid-solid interface and partial differential equation of potential flow are applied to calculate the fluid pressure. Classical plate theory is used for formulating nano-plate. By using nonlocal elasticity theory, small size effect is considered for nano-plates. The fluid flow is considered to be homogeneous, laminar, fully developed, incompressible, isothermal, uni-directional (along the length of nano-plate) and continuous. Then, by considering the effect of Knudsen (Kn) and slip boundary condition, the effect of nano-size is considered for fluid flow. Kn affects the dimensionless velocity correction factor (VCF) parameter directly. It is defined as the ratio of average sliding fluid velocity to average no-slip fluid velocity. Approximate solutions are computed by using Galerkin’s weighted residuals method. By considering the effects of nonlocal parameter and Kn, the critical velocity would reduce. Nonlocal parameter could have more effect on reducing the divergence critical velocity of upper modes and coupled-mode flutter. By comparing the effects of Kn and nonlocal parameter, we notice that whenever the fluid is a liquid, most of the contribution in decreasing critical flow velocity is due to nonlocal parameter whole and whenever the fluid is a gas, Kn has a greater role in decreasing the critical velocity. For plate aspect ratios less than 1, i.e., increasing the width of plate, the total plate stiffness would decrease and natural frequencies would become lower than frequencies corresponding to a square plate. For plate aspect ratios more than 1, i.e., decreasing the width of the plate, the total plate stiffness would increase and the natural frequencies would become larger than corresponding frequencies of a square plate. In summary, plate aspect ratio could have impressive effects on the critical flow velocities, the temporal order of happening these instabilities, and the type of observed instabilities. For example, increasing aspect ratio could shift the mechanism of instability from a flutter mode toward a divergence one. () Keywords : small-size effect, fluid-structure interaction , nano-plate, slip boundary condition,nonlocal theory, divergence, flutter, Knudsen number
