A novel nonlocal higher-order theory for the accurate vibration analysis of 2D FG nanoplates

Abstract

In this paper, vibration analysis of the 2 D-FG nanoplate is studied based on a novel higher-order shear deformation theory (HSDT). The proposed HSDT is a composition of trigonometric, exponential and polynomial functions which is one of the most accurate HSDTs. The mechanical properties of the nanoplate change along with the length and thickness directions, according to arbitrary functions. To model the displacement field, the impacts of both transverse shear and thickness stretching are considered. To consider the small-scale impact, nonlocal elasticity theory is applied. To obtain the equations of motion, Hamilton’s principle is applied. Navier method is used for a closed-form solution of the 2 D-FG nanoplates with simply-supported boundary conditions. The impact of different parameters including the small-scale parameter are studied on the natural frequency of the system. The results illustrate that when size effect parameter is smaller/greater than 0.5 nm, the impacts of the FG parameters on the frequency of the system increase/reduce.