Nonlinear bending and vibration analyses of FG nanobeams considering thermal effects

Abstract

Nonlinear bending and nonlinear free vibration analysis are presented for FG nanobeams based on physical neutral surface concept and high-order shear deformation beam theory with a von Kármán-type equations and including thermal effects. The material properties are temperature-dependent and vary in the thickness direction. Nonlinear bending approximate solutions and free vibration solutions for present model with fixed supported boundary conditions are given out by a two-step perturbation method. Some comparisons are presented to valid the reliability of the present study. In numerical analysis, the effects of the volume fraction, nonlocal parameter, strain gradient parameter, and temperature changes on nonlinear bending and vibration are investigated.