The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

Abstract

A comprehensive vibrational analysis of bi-directional functionally graded (2D-FG) rotating nanobeams with porosities is studied for the first time. The beam is modeled based on general nonlocal theory (GNT) where the beam governing equations are derived depending on two different nonlocal parameters. Unlike Eringen’s conventional form of nonlocal theory, the general nonlocal theory can reveal both hardening and softening behaviors of the material. Here, the attenuation functions are altered in both transverse and longitudinal directions of 2D-FG nanobeam. This feature, which has a significant effect on the vibrational characteristics, has not been considered in previous studies. Moreover, to estimate the effects of the higher-order transverse shear strains on the vibration of the nanobeam, Reddy’s beam theory (RBT), which includes higher-order shear deformation, is employed. The material properties of the 2D-FG rotating nanobeam vary both in the length and thickness directions according to a power law. The generalized differential quadrature method (GDQM) is used to predict the vibration response. Also, the effects of material variation along the length and thickness directions, the rotating velocity of the nanobeam, the porosity volume fraction and the length to thickness ratio of the rotating nanobeam are illustrated and discussed in detail. The investigations performed in this study expose new phenomena for the vibration of nanobeams.