In the current study, the modified shear deformation theories are used for analyzing the electro-mechanical vibration of inhomogeneous piezoelectric nanoplates in conjunction with the nonlocal elasticity theory. These theories not only satisfy transverse shear traction-free conditions on the top and bottom surfaces of the plate but also consider exponential and trigonometric distributions for the transverse shear deformations. Heterogeneity of the structure is supposed to be in the thickness direction of the nanoplate and it is assumed that the simply supported functionally graded piezoelectric nanoplate is subjected to a biaxial force and an external electric voltage. The governing equations of the vibrating functionally graded piezoelectric nanoplate are obtained by using Hamilton’s principle, which are then solved by using Navier’s method to achieve the vibrational behavior of the structure. The detailed discussion is presented to explain the influences of the various parameters on the natural frequencies of functionally graded piezoelectric nanoplates. It is concluded that increasing gradient index parameter, nonlocal parameter, thickness ratio and compressive forces lead to a decrease in natural frequencies while rising tensile forces and aspect ratio increase the natural frequencies.
