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.

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

“…Structures and components in advanced machines such as aerospace shuttles and craft require advanced composites whose properties vary continuously in more than one direction to satisfy the requirements of temperature and stress distributions in two or more directions [27]. By the rapid advancement in nanomechanics, the static and dynamic characteristics of bi-directional functionally graded (BDFG) micro/nanosized beams have been modelled and investigated based on the differential nonlocal elasticity theory "DNET" ( [6,[28][29][30][31][32][33][34]), MCST ( [35][36][37][38][39][40][41][42]), and the differential nonlocal strain gradient theory "DNSGT" ( [43][44][45]).…”

Analysis of the magneto-thermoelastic vibrations of rotating Euler- Bernoulli nanobeams using the nonlocal elasticity model

“…Using nonlocal and nonclassical continuous mechanics, Narendar [12] established a rotating single-walled nanotube (SWCNT) model by simulating it as an Euler-Bernoulli beam. Rahmani et al [13] created a GNT and RBT-based vibrational analysis for 2D-FG spinning nanobeams with pore sizes. Further, the 2D-FG porous model and a unique hybrid approach utilizing long-range interatomic responses are created.…”

Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model

“…[61][62][63][64][65] Few researchers emphasized the influence of porosity on stress, electric field, bending, bifurcation buckling, linear, and nonlinear vibrations of nano-beams. [66][67][68][69][70][71][72] Recently, Rahmani et al 73 studied the vibration characteristics of porous nano-beams in rotational motion, and Rastehkenari et al 74 studied the nonlinear random vibrations of FGMs porous nano-beams. Zhao et al 75 studied the effects of porosity on the bending and free vibration analysis of axially graded flexoelectric nano-beams.…”