Free vibration of FG nanobeam using a finite‐element method

Abstract

In this work, a non-local finite-element formulation is developed to analyse free vibration of functionally graded (FG) nanobeams considering power-law variation of material through thickness of the nanobeam. The Euler-Bernoulli beam theory based on Eringen's non-local elasticity theory with one length scale parameter is used to model the FG nanobeam. To this end, two types of FG nanobeams composed of two different materials are analysed by using the developed non-local finite-element formulation. First FG nanobeam is made of alumina (Al 2 O 3) and steel, whereas second one is composed of silicon carbide (SiC) and stainless steel (SUS304). Numerical results are presented to show the effect of power-law exponent (k) and nanostructural length scale (e 0 a/L) on the free vibration of FG nanobeams.

Comparative Stability Analysis of Boron Nitride Nanotube using MD Simulation and Nonlocal Elasticity Theory

“…More recently, Zhang and Zhou studied the buckling behavior of boron nanotube which compose only from boron atoms [14]. To analyze nanotubes by taking the size effect into consideration, many methods have been used such as couple stress theory [15,16], strain gradient theory, nonlocal elasticity theory [17][18][19][20][21][22], surface elasticity theory, nonlocal surface elasticity theory [23], DSC method [24][25][26][27][28][29]. Furthermore, many research have been done studying vibration behavior of nanostructures [30][31][32][33].…”

Free vibration analysis of nanotube based sensors including rotary inertia based on the Rayleigh beam and modified couple stress theories

“…have recently been used frequently, as they contribute to overcome deficiencies that cannot be compensated by classical theories and achieving more accurate results. Papers about size dependent nonclassical analyzes of nano / micro-sized structures for instance nanotubes (Civalek et al 2020;Uzun et al 2018;2020a;Yaylı 2019;Mercan and Civalek 2017), functionally graded (FG) nanobeams/microbeams (Ebrahimi et al 2019;Uzun et al 2020b;Gorgani et al 2019;Uzun and Yaylı 2020;Akgöz and Civalek 2017;Akbaş 2017Akbaş , 2018a, nanowires (Uzun and Civalek 2019a,b), nanorods (Yaylı 2018b(Yaylı , 2019Akbaş 2019Akbaş , 2020, nanobeams/microbeams (Miandoab 2015;Akbaş 2016Akbaş , 2018b, microtubules (Demir and Civalek 2013;Civalek and Demir 2016), micro-pipes (Hosseini and Bahaadini 2016), microbars (Akgöz and Civalek 2014), FG microplates (Thai et al 2017;Farzam and Hassani 2019) are available in the literature.…”

Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions

“…Longitudinal vibrations of conical and cylindrical rods have been presented by Fedeto et al [29] and Marais et al [30] based on the Rayleigh-Bishop theory. In addition to the nanorods [31][32][33], nanotubes [34][35][36][37][38][39][40], nanowires [41,42], functionally graded nanobeams/microbeams [43][44][45][46], nanobeams [47][48][49][50][51][52], microcolumns [53] and microbeams [54], which are the other one dimensional ultra-small structures, have been studied extensively with various non-classical elasticity theories which captured the small-scale effect.…”