Abstract: The transverse free vibration characteristics of a two-dimensional nanoplate with axial velocity are investigated based on the nonlocal strain gradient theory. The vibration control equations for the in-plane advection of the system are established accord? ing to the generalized Hamilton’s principle， and the intrinsic frequency of the nanoplate is derived by using complex modal analysis in the case of a four-ended simple support. The critical velocity of the system is determined by the equilibrium solution of the con? trol equations， and the real and imaginary parts of the first-fourth-order modal functions are further analyzed for both the sub-critical and the supercritical velocities. The numerical results show that the scaling effect leads to a change in the self-oscillation frequency of the system at the micro- and nanoscale， and the nonlocal and strain gradient parameters have ‘softening’ and ‘hardening’ effects on the equivalent stiffness of the nanoplates， respectively， which affects the intrinsic frequency and the modal function of the nano? plates. This affects the intrinsic frequency and mode function of the nanoplates， and the higher order frequencies and vibration modes are more significantly affected by the size parameters.