Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches

Abstract

The buckling and free vibrations of rectangular nanoplates are considered in the present paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. Besides, the analysis involve the nonlocal strain and stress theories of elasticity to take into account the small-scale effects encountered in nanostructures/nanocomposites. Hamilton’s principle is used to establish the governing equations of the nanoplate. The Rayleigh-Ritz method is proposed to solve eigenvalue problems dealing with the buckling and free vibration analysis of the nanoplates considered. Some examples are presented to investigate and illustrate the effects of various formulations.

Keywords

• nonlocal stress theory
• nonlocal strain theory
• buckling
• free vibrations
• nanoplates
• higher order shear deformation theories