Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

Abstract

By taking the effect of the scale parameter explicitly into account, bending behavior of Euler‐Bernoulli and Timoshenko nanobeams is studied using doublet mechanics. In addition, the effect of chirality on the softening or hardening behavior of an Euler‐Bernoulli nanobeam in bending is studied by taking the effect of the chiral angle explicitly into account. For the bending of the Timoshenko nanobeam the effect of the scale parameter and chirality on the axial and shear stresses is studied and the results are compared with the gradient and Eringen‐like models. It is shown that as the chiral angle increases, a simply supported Timoshenko nanobeam under a uniform loading changes from a softening to a hardening nanobeam indicating that chirality has a pronounced effect on the bending response of the nanobeams.

Advances in modelling and analysis of nano structures: a review

“…Ebrahimian et al [166] studied the effect of chirality on the softening or hardening behavior of a Euler-Bernoulli and Timoshenko nanobeams in bending. Incorporation of the scale parameter and chiral angle makes the nanobeam softer.…”

Assessment of machine learning methods predicting the axial vibration frequencies of microbars

“…In order to overcome these disadvantages, higher-order continuum theories such as surface elasticity, nonlocal elasticity, doublet mechanics, strain gradient elasticity, modified couple stress theories, and others were proposed to study the size effect at small scales. Looking at the literature, it becomes evident that researchers have readily adopted these theories as supported by the conducted studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Finite element model for free vibration analysis of curved zigzag nanobeams

“…The axial vibration of CNTs considering elastic boundary conditions and damping were studied in [88,89]. The effect of the chirality was considered for the investigation of flexural responses of nanobeams using the Classical Beam Theory (CBT) and First-order Beam Theory (FBT) theories [90,91]. The CBT was also employed for the flexural and free vibration of CNTs by Eltaher and Mohamed [92,93].…”

“…In a recent study, Karamanli [94] presented FEDM for the structural behaviors of nanobeams. The literature review mentioned above [82][83][84][85][86][87][88][89][90][91][92][93][94] indicates that the DM theory has been employed for only straight nanobeams, which implies there is a gap for curved ones. This paper aims to fill it by investigating the free vibration behaviours of curved nanobeams, which is the main contribution and novelty of this study.…”