Nonlinear Strain Gradient Theory Based Vibration and Instability of Boron Nitride Micro-Tubes Conveying Ferrofluid

Abstract

Nonlinear vibration and instability of a boron nitride micro-tube (BNMT) conveying ferrofluid under the combined magnetic and electric fields are investigated. Based on Euler–Bernoulli beam (EBB), piezoelasticity strain gradient theory and Hamilton's principle, high order equations of motion are derived for three boundary conditions namely as clamped–clamped (C–C), simply–simply (S–S) and clamped–simply (C–S). The differential quadrature method (DQM) is applied to discretize the motion equations in order to obtain the nonlinear frequency and critical fluid velocity using a direct iterative method. A detailed parametric study is conducted to elucidate the influences of the various boundary conditions, size diameter and magnetic field on vibrational characteristic of BNMT. Numerical results indicate that the effect of magnetic field appears in higher speed of ferrofluid and increases the critical velocity or enlarges the stability region. The results are in good agreement with the previous researches. The results of this study can be used to manufacture smart micro/nano electromechanical systems in advanced biomechanics applications with magnetic and electric fields as parametric controllers.

Hygro-thermo-mechanical vibration of two vertically aligned single-walled boron nitride nanotubes conveying fluid

“…So far, several studies have used the mentioned nonclassical continuum models to consider the impacts of low scales on the free/forced vibration and static/dynamic instability of different nanobeams, nanoplates, CNTs, and BNNTs (Apuzzo et al, 2019; Ansari et al, 2012; Ansari and Gholami, 2017; Arani et al, 2012, 2016, 2019; Arani and Roudbari, 2014; Azarboni, 2019; Bahaadini et al, 2017, 2018; Gholami and Ansari, 2018; Ghorbanpour Arani et al, 2014, 2016; Jam et al, 2012; Jena et al, 2020b, 2020a; Jena et al, 2021, 2019a, 2019b; Jena and Chakraverty, 2019; Jorshari et al, 2019; Kamarian et al, 2016; Mohammadimehr et al, 2016, 2018; Reza et al, 2012; Roudbari and Jorshari, 2018; Saffari et al, 2020; Sedighi, 2020; Sedighi et al, 2020; Shishesaz et al, 2020; Simsek, 2011; Tyagi et al, 2019). Using the nonlocal elasticity theory of Eringen (1983) based on the Euler–Bernoulli beam assumption, Arani and Roudbari (2013) proposed a nonclassical model to study the effects of surface stress and small scales on the nonlocal frequencies of zigzag-coupled SWBNNTs in a viscoelastic medium.…”

Stress Analysis of a Functionally Graded Micro/ Nanorotating Disk with Variable Thickness Based on the Strain Gradient Theory

“…The classical models which do not consider the size effect in micro-structures fail to predict the results reported in the conducted experimental efforts, while new models including additional parameters capable of accounting for the size effect succeed in reproducing the appropriate results. Some non-classical continuum theories can be mentioned as non-local [Eringen, 1999[Eringen, , 2002, strain gradient [Ghorbanpour et al, 2014;Sedighi et al, 2014;Toupin, 1965] and couple stress theory [Toupin, 1962]. Fleck and Hutchinson [2001] reformulated the higher-order continuum theory presented by Mindlin and Eshel [1968] called as the strain gradient theory.…”

Nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM

“…Nonlinear free vibration of micro-plates was studied by Ramezani [15] based on a strain gradient elasticity theory. Nonlinear vibration and instability of a boron nitride micro-tube (BNMT) conveying ferrofluid under the combined magnetic and electric fields were investigated by Ghorbanpour et al [16] . In another work by Ghorbanpour et al [17] , nonlinear vibration and instability analysis of a bonded double-smart composite microplate system (DSCMPS) conveying microflow based on nonlocal piezoelasticity theory were presented.…”