This paper aims to study the influence of material uncertainties on thermo-elastic vibration response of functionally graded porous (FGP) beams reinforced with graphene platelets (GPLs) using the perturbation-based stochastic finite element method. The influence of material uncertainty on the vibration behavior of FGP-GPL reinforced beams subjected to thermal loading conditions have been discussed for low variability (randomness) in material design parameters (porosity content, amount of nanofillers) and material properties (Young’s modulus, density of metal matrix, and nanofillers) respectively. A C0 continuous stochastic finite element formulation based on higher-order shear deformation theory has been formulated. The convergence and validation of the present formulation have been compared with a traditional Monte-Carlo simulation to establish the accuracy of the present methodology. The homogenized effective material properties are estimated using the Halpin-Tsai micromechanics model and Voigt’s rule of mixture and are typically assumed to be varying along the thickness direction. The results highlighting the effect of uncertainty in material properties on the thermo-elastic vibration response of FGP-GPL reinforced beams have been discussed thoroughly.
PollienACondeYPambaguianL, et al. Graded open-cell aluminium foam core sandwich beams. Mater Sci Eng A2005; 404: 9–18.
2.
HangaiYSaitoKUtsunomiyaT, et al. Compression properties of Al/Al-Si-Cu alloy functionally graded aluminum foam fabricated by friction stir processing route. Mater Trans2013; 54: 405–408.
3.
HassaniAHabibolahzadehABaftiH.Production of graded aluminum foams via powder space holder technique. Mater Des2012; 40: 510–515.
4.
HangaiYTakahashiKUtsunomiyaT, et al. Fabrication of functionally graded aluminum foam using aluminum alloy die castings by friction stir processing. Mater Sci Eng A2012; 534: 716–719.
5.
BanhartJ.Manufacture, characterisation and application of cellular metals and metal foams. Prog Mater Sci2001; 46: 559–632.
6.
LefebvreLPBanhartJDunandDC.Porous metals and metallic foams: current status and recent developments. Adv Eng Mater2008; 10: 775–787.
7.
BettsC.Benefits of metal foams and developments in modelling techniques to assess their materials behaviour: a review. Mater Sci Technol2012; 28: 129–143.
8.
ZhaoSZhaoZYangZ, et al. Functionally graded graphene reinforced composite structures: a review. Eng Struct2020; 210: 110339.
9.
RafieeMARafieeJWangZ, et al. Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano2009; 3: 3884–3890.
10.
ChuKJiaC.Enhanced strength in bulk graphene-copper composites. Phys Status Solidi2014; 211: 184–190.
11.
KitipornchaiSChenDYangJ.Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater Des2016; 116: 656–665.
12.
ChenDYangJKitipornchaiS.Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams. Compos Sci Technol2017; 142: 235–245.
13.
AnirudhBGanapathiMAnantC, et al. A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: bending, vibration and buckling. Compos Struct2019; 222: 110899.
14.
GanapathiMAnirudhBAnantC, et al. Dynamic characteristics of functionally graded graphene reinforced porous nanocomposite curved beams based on trigonometric shear deformation theory with thickness stretch effect. Mech Adv Mater Struct2021; 28: 741–752.
15.
LiZZhengJZhangZ.Mechanics of the confined functionally graded porous arch reinforced by graphene platelets. Eng Struct2019; 201: 109817.
Jedari SalamiS. Large deflection geometrically nonlinear bending of sandwich beams with flexible core and nanocomposite face sheets reinforced by nonuniformly distributed graphene platelets. J Sandw Struct Mater2020; 22: 866–895.
18.
ManickamGGuptaPDeS, et al. Nonlinear flexural free vibrations of size-dependent graphene platelets reinforced curved nano/micro beams by finite element approach coupled with trigonometric shear flexible theory. Mech Adv Mater Struct2020; 29: 2489–2515.
19.
YasMHRahimiS.Thermal buckling analysis of porous functionally graded nanocomposite beams reinforced by graphene platelets using Generalized differential quadrature method. Aerosp Sci Technol2020; 107: 106261.
20.
YangZWuDYangJ, et al. Dynamic buckling of rotationally restrained FG porous arches reinforced with graphene nanoplatelets under a uniform step load. Thin-Walled Struct2021; 166: 1–11.
21.
ShakirMTalhaM. Influence of material uncertainty on higher-order FG-GPLs reinforced porous spherical panels under blast loading. Thin-Walled Structures, 2022; 176: 109319.
22.
WangYFengCYangJ, et al. Nonlinear vibration of FG-GPLRC dielectric plate with active tuning using differential quadrature method. Comput Methods Appl Mech Eng2021; 379: 113761.
23.
WangYFengCYangJ, et al. Static response of functionally graded graphene platelet–reinforced composite plate with dielectric property. J Intell Mater Syst Struct2020; 31: 2211–2228.
24.
TengMWWangYQ.Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets. Thin-Walled Struct2021; 164: 107799.
25.
ChaiQWangYQ.Traveling wave vibration of graphene platelet reinforced porous joined conical-cylindrical shells in a spinning motion. Eng Struct2022; 252: 113718.
26.
YeCWangYQ.Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: internal resonances. Nonlinear Dyn2021; 104: 2051–2069.
27.
XuHWangYQZhangY.Free vibration of functionally graded graphene platelet-reinforced porous beams with spinning movement via differential transformation method. Arch Appl Mech2021; 91: 4817–4834.
28.
WangYQ.Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state. Acta Astronaut2018; 143: 263–271.
29.
WangYQYeCZuJW.Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets. Aerosp Sci Technol2019; 85: 359–370.
30.
HaboussiMSankarAGanapathiM.Nonlinear axisymmetric dynamic buckling of functionally graded graphene reinforced porous nanocomposite spherical caps. Mech Adv Mater Struct2019; 28: 1–14.
31.
GaoKDoDMLiR, et al. Probabilistic stability analysis of functionally graded graphene reinforced porous beams. Aerosp Sci Technol2020; 98: 105738.
32.
YangJLiewKMKitipornchaiS.Stochastic analysis of compositionally graded plates with system randomness under static loading. Int J Mech Sci2005; 47: 1519–1541.
33.
LalASinghBN.Stochastic free vibration of laminated composite plates in thermal environments. J Thermoplast Compos Mater2010; 23: 57–77.
34.
TalhaMSinghBN.Stochastic perturbation-based finite element for buckling statistics of FGM plates with uncertain material properties in thermal environments. Compos Struct2014; 108: 823–833.
35.
TalhaMSinghBN.Stochastic vibration characteristics of finite element modelled functionally gradient plates. Compos Struct2015; 130: 95–106.
36.
ShakirMTalhaM.Influence of material stochasticity on buckling characteristics of initially imperfect higher-order shear deformable gradient plates. Int J Struct Stab Dyn2021; 22: 2150004.
37.
XuYQianYSongG.Stochastic finite element method for free vibration characteristics of random FGM beams. Appl Math Model2016; 40: 10238–10253.
38.
García-MacíasECastro-TrigueroRFriswellMI, et al. Metamodel-based approach for stochastic free vibration analysis of functionally graded carbon nanotube reinforced plates. Compos Struct2016; 152: 183–198.
39.
NguyenHXDuy HienTLeeJ, et al. Stochastic buckling behaviour of laminated composite structures with uncertain material properties. Aerosp Sci Technol2017; 66: 274–283.
40.
PouresmaeeliSFazelzadehSAGhavanlooE, et al. Uncertainty propagation in vibrational characteristics of functionally graded carbon nanotube-reinforced composite shell panels. Int J Mech Sci2018; 149: 549–558.
41.
WuDLiuAHuangY, et al. Mathematical programming approach for uncertain linear elastic analysis of functionally graded porous structures with interval parameters. Compos B: Eng2018; 152: 282–291.
42.
GaoKLiRYangJ.Dynamic characteristics of functionally graded porous beams with interval material properties. Eng Struct2019; 197: 109441.
LiuZYangMChengJ, et al. Stochastic isogeometric analysis for the linear stability assessment of plate structures using a Kriging enhanced neural network. Thin-Walled Struct2020; 157: 107120.
45.
KhayatMBaghlaniANajafgholipourMA.The propagation of uncertainty in the geometrically nonlinear responses of smart sandwich porous cylindrical shells reinforced with graphene platelets. Compos Struct2021; 258: 113209.
46.
LiuZYangMChengJ, et al. Meta-model based stochastic isogeometric analysis of composite plates. Int J Mech Sci2021; 194: 106194.
47.
BaghlaniANajafgholipourMAKhayatM.The influence of mechanical uncertainties on the free vibration of functionally graded graphene-reinforced porous nanocomposite shells of revolution. Eng Struct2021; 228: 111356.
48.
KhayatMBaghlaniANajafgholipourMA.The probabilistic dynamic stability analysis of fluid-filled porous cylindrical shells reinforced with graphene platelets. Thin-Walled Struct2021; 167: 108256.
49.
RobertsAPGarbocziEJ.Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Mater2001; 49: 189–197.
50.
AffdlJCHKardosJL. The Halpin-Tsai equations: a review. Polym Eng Sci1976; 16: 344–352.
HeyligerPRReddyJN.A higher order beam finite element for bending and vibration problems. J Sound Vib1988; 126: 309–326.
53.
CookRD.Application of finite element analysis. Elastomerics1987; 119: 18–23.
54.
TalhaMSinghBN.Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl Math Model2010; 34: 3991–4011.
55.
AmirMTalhaM.Thermoelastic vibration of shear deformable functionally graded curved beams with microstructural defects. Int J Struct Stab Dyn2018; 18: 1850135.
56.
NguyenTKNguyenBDVoTP, et al. Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams. Compos Struct2017; 176: 1050–1060.
57.
WattanasakulpongNGangadhara PrustyBKellyDW.Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams. Int J Mech Sci2011; 53: 734–743.
58.
ChaPDGuW.Comparing the perturbed Eigensolutions of a generalized and a standard Eigenvalue problem. J Sound Vib1999; 227: 1122–1132.
59.
ShainaPRGeorgeLYadavV, et al. Estimating the thermal expansion coefficient of graphene: the role of graphene-substrate interactions. J Phys Condens Matter2016; 28: 085301.
60.
YasMHRahimiS.Thermal vibration of functionally graded porous nanocomposite beams reinforced by graphene platelets. Appl Math Mech2020; 41: 1209–1226.
