Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

Abstract

A novel functionally graded (FG) polymer-based nanocomposite reinforced by graphene nanoplatelets is proposed based on a new distribution law, which is constructed by the error function and contains a gradient index. The variation of the gradient index can result in a continuous variation of the weight fraction of graphene nanoplatelets (GPLs), which forms a sandwich structure with graded mechanical properties. The modified Halpin–Tsai micromechanics model is used to evaluate the effective Young’s modulus of the novel functionally graded graphene nanoplatelets reinforced composites (FG-GPLRCs). The bending and elastic vibration behaviors of the novel nanocomposite beams are investigated. An improved third order shear deformation theory (TSDT), which is proven to have a higher accuracy, is implemented to derive the governing equations related to the bending and vibrations. The Chebyshev–Ritz method is applied to describe various boundary conditions of the beams. The bending displacement, stress state, and vibration frequency of the proposed FG polymer-based nanocomposite beams under uniformly distributed loads are provided in detail. The numerical results show that the proposed distributions of GPL nanofillers can lead to a more effective pattern of improving the mechanical properties of GPL-reinforced composites than the common ones.

Nanobeams with Internal Discontinuities: A Local/Nonlocal Approach

“…The behaviour of materials at the nanoscale level is significantly different from that exhibited by the same materials at the macroscale level [ 2 , 3 , 4 , 5 , 6 ]. In order to both analyse the so-called size effect and properly evaluate the size-dependent properties, two approaches may be followed: experimental characterisation [ 7 , 8 , 9 ] and theoretical modelling [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ]. For instance, the tensile yield strength of a gradient nano-grained (GNG) surface layer in a bulk coarse-grained (CG) rod of a face-centred cubic Cu was investigated by Fang et al [ 7 ], who observed an increment of strength of about 100% with respect to that of a CG Cu.…”

“…However, despite their high level of reliability, performing experimental tests at the nanoscale may be quite expensive and time consuming, leading to often prefer theoretical models that are reliable and low-cost tool to estimate the behaviour of the nanomaterials. As a matter of fact, several theoretical models have been proposed aiming to capture the small-scale effect on the static [ 10 , 11 , 12 , 13 , 14 , 15 ] and dynamic responses [ 11 , 12 , 13 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ], instability [ 12 , 24 , 25 , 26 , 27 , 28 ] and fracture behaviour [ 10 , 29 , 30 ] of nanomaterials at both the micro- or nano-scale level. In addition, the stress-driven nonlocal integral model (SDM) is available in the literature [ 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ].…”

Nonlinear Free and Forced Vibrations of a Hyperelastic Micro/Nanobeam Considering Strain Stiffening Effect

“…For many decades, vibration analysis of mechanical structures was a major topic among scientists [1][2][3][4][5][6][7][8][9][10]. Over recent decades, a surge of interest in studying hyperelastic materials was shown.…”

Dynamic Response of Multilayered Polymer Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) Nano-Beams in Hygro-Thermal Environment

“…Notwithstanding a number of studies have been carried out on the mechanical behavior of macroscopical structures like beams [14][15][16][17][18][19][20], plates and shells [21][22][23][24][25], made of functionally graded carbon nanotubes (FG-CNTRC) or graphene nanoplatelets reinforced -A slender and perfectly straight nano-beam of a Euler-Bernoulli type, with a rectangular cross-section, is considered; hence, the influence of thickness stretching and shear deformation are neglected; -…”

“…Notwithstanding a number of studies have been carried out on the mechanical behavior of macroscopical structures like beams [ 14 , 15 , 16 , 17 , 18 , 19 , 20 ], plates and shells [ 21 , 22 , 23 , 24 , 25 ], made of functionally graded carbon nanotubes (FG-CNTRC) or graphene nanoplatelets reinforced composites (FG-GNPRC), there is relatively little scientific knowledge about their size-dependent mechanical response at small scale. The FG-CNTRC nano-beam has become a potential candidate for a wide variety of nanosystems and the size effects on their statical and dynamic response should be further developed.…”