Bending and Vibration Analysis of the FG Circular Nanoplates Subjected to Hygro-Thermo-Electrical Loading Based on Nonlocal Strain Gradient Theory

Abstract

This paper examines the deflection and vibration of the circular nanoplates made of functionally graded (FG) materials. The material properties of the system vary across the thickness based on the power-law distribution. The system is assumed to be subjected to hygro-thermo-electrical loadings based on nonlinear relations. The first-order shear deformation theory (FSDT) is applied to model the circular plate as a continuous system. The nonlocal strain gradient theory is employed to consider the small-scale impacts. The dynamic equations of the motion of the FG circular nanoplate for diverse boundary conditions are derived using Hamilton’s principle, and the differential quadrature (DQ) procedure is used to obtain the deflection and frequency of the system in a discrete state. The effects of various parameters, such as small-scale factors, FG material characteristics, external voltage, and hygro-thermal loadings, on the vibration of FG circular nanoplates are explored.