In the present study, the influence of aeroelastic force on the free vibration of a piezoelectric nanoplate in contact with a bounded fluid with fully simply supported boundary conditions and fully clamped boundary conditions is investigated. To model the structure, a nonlocal elasticity theory based on modified shear theories with various thickness-wise distributions for shear deformation, including exponential, triangular, and two new distribution functions introduced by the authors of this paper for the first time, is employed. The fluid considered in this analysis is assumed to be incompressible, inviscid, and irrotational, and the effects of the free-surface waves of the fluid are neglected. The aerodynamic force exerted by the airflow on the nanoplate is also modeled using first-order Piston theory. The fluid velocity potential is obtained by solving Laplace’s equation while satisfying the fluid boundary conditions, and by applying Hamilton’s principle, the governing equations for the vibrational behavior of the system are derived. After solving the equations using the Galerkin weighted residual method, numerical results are compared with published results in reputable articles to demonstrate the accuracy of the model and relationships presented in this study. Finally, the effects of various parameters, such as the geometric dimensions of the nanoplate, the nonlocal parameter, temperature variations, electric loading, fluid depth, reservoir width, aerodynamic pressure, boundary conditions, and the type of transverse shear deformation distribution along the thickness, on the frequencies and mode shapes of the vibrations are analyzed.