This study deals with the dynamic behavior of short-fiber reinforced composite nanobeams. It is assumed that short-fibers are aligned or randomly distributed in the composite nanobeams. Nonlocal strain gradient theory is applied to composite nanobeam mechanics including Euler–Bernoulli and Timoshenko beam models. The transverse vibration of these composite nanobeams is investigated for various boundary conditions. Approximate Ritz method is used for obtaining the natural frequencies of short-fiber reinforced composite nanobeams. In addition to vibration analysis, wave propagation in short-fiber reinforced composite nanobeams is investigated and wave dispersion relations are analytically obtained for both Euler-Bernoulli and Timoshenko beam models. The vibration and wave dispersion results of short-fiber reinforced composite nanobeams are obtained for aligned and randomly distributed cases. The results obtained from this paper showed that there is no significant difference between the aligned and randomly oriented short-fiber composite nanobeams. This provides great convenience to designers where it is not possible to orient the reinforcement material in composites. The present study may be useful for the mechanical analysis and design of micro/nano-electromechanical systems (MEMS/NEMS), nanoprobes, nanosensors, nanoactuators, and atomic force microscopes.
AgarwalBDBroutmanLJ (eds). Analysis and performance of fiber composites. 2nd ed.New Delhi: John Wiley & Sons, 1990.
2.
MindlinRTierstenH. Effects of couple-stresses in linear elasticity. New York, NY: Columbia University, 1962.
3.
EringenAC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys1983; 54(9): 4703–4710.
4.
MindlinRD. Micro-structure in linear elasticity. Arch Ration Mech Anal1964; 16(1): 51–78.
5.
GranikV. Microstructural mechanics of granular media. Technique Report IM/MGU Institute of Mechanics of Moscow State University, 1978, pp.78–241.
6.
SillingSA. Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids2000; 48: 175–209.
7.
LimCWZhangGReddyJN. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids2015; 78: 298–313.
8.
LiXWeiYLuL, et al. Dislocation nucleation governed softening and maximum strength in nano-twinned metals. Nature2010; 464: 877–880.
LiLHuYLingL. Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Compos Struct2015; 133: 1079–1092.
11.
EbrahimiFBaratiMR. Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory. J Therm Stresses2016; 39(12): 1560–1571.
12.
LiLLiXHuY. Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci2016; 102: 77–92.
13.
EbrahimiFBaratiMR. Vibration analysis of viscoelastic inhomogeneous nanobeams incorporating surface and thermal effects. Appl Phys A2017; 123: 5.
14.
EbrahimiFBaratiMR. A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams. Compos Struct2017; 159: 174–182.
15.
EbrahimiFBaratiMR. Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory. Compos Struct2017; 159: 433–444.
16.
LuLGuoXZhaoJ. A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms. Int J Eng Sci2017; 119: 265–277.
17.
Bakhshi KhanikiHHosseini-HashemiS. Dynamic transverse vibration characteristics of nonuniform nonlocal strain gradient beams using the generalized differential quadrature method. Eur Phys J Plus2017; 132: 500.
18.
HadiANejadMZHosseiniM. Vibrations of three-dimensionally graded nanobeams. Int J Eng Sci2018; 128: 12–23.
19.
WangJShenHZhangB, et al. Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory. Physicae2018; 101: 85–93.
20.
MalikanMNguyenVBTornabeneF. Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory. Eng Sci Technol Int J2018; 21: 778–786.
21.
RajasekaranSKhanikiHB. Bending, buckling and vibration analysis of functionally graded non-uniform nanobeams via finite element method. J Braz Soc Mech Sci Eng2018; 40: 459.
22.
FakherMHosseini-HashemiS. Bending and free vibration analysis of nanobeams by differential and integral forms of nonlocal strain gradient with Rayleigh–Ritz method. Mater Res Express2017; 4(12): 125025.
23.
ŞimşekM. Some closed-form solutions for static, buckling, free and forced vibration of functionally graded (FG) nanobeams using nonlocal strain gradient theory. Compos Struct2019; 224: 1–17.
24.
KaramiBJanghorbanMRabczukT. Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory. Compos B2020; 182: 1–12.
25.
WuQChenHGaoW. Nonlocal strain gradient forced vibrations of FG-GPLRC nanocomposite microbeams. Eng Comput2020; 36: 1739–1750.
26.
GholipourAGhayeshMHHussainS. A continuum viscoelastic model of Timoshenko NSGT nanobeams. Eng Comput2022; 38: 631–646.
27.
EbrahimiFBaratiMR. Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory. Appl Phys A2016; 122: 843.
28.
EbrahimiFBaratiMR. Through-the-length temperature distribution effects on thermal vibration analysis of nonlocal strain-gradient axially graded nanobeams subjected to nonuniform magnetic field. J Therm Stresses2017; 40(5): 548–563.
29.
EbrahimiFBaratiMR. Vibration analysis of viscoelastic inhomogeneous nanobeams resting on a viscoelastic foundation based on nonlocal strain gradient theory incorporating surface and thermal effects. Acta Mech2017; 228: 1197–1210.
30.
EbrahimiFBaratiMR. Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory. Mech Adv Mater Struct2018; 25(4): 350–359.
31.
MohammadianMHosseiniSMAbolbashariMH. Lateral vibrations of embedded hetero-junction carbon nanotubes based on the nonlocal strain gradient theory: analytical and differential quadrature element (DQE) methods. Physicae2019; 105: 68–82.
32.
Ghorbani ShenasAZiaeeSMalekzadehP. A unified higher-order beam theory for free vibration and buckling of FGCNT-Reinforced microbeams embedded in elastic medium based on unifying stress–strain gradient framework. Iran J Sci Technol Trans Mech Eng2019; 43: 469–492.
33.
ZhaoJLiXLiS, et al. Size-dependent investigation of the 2D-FG CNTRC nanobeams using nonlocal strain gradient beam theory subjected to hygro-thermo conditions. Waves Random Complex Media2022; 1–20. DOI: 10.1080/17455030.2022.2070682
34.
EnayatSHashemianMToghraieD, et al. Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects. J Appl Math Mech2020: 1–31. DOI: 10.1002/zamm.202000231
35.
GülU. Transverse free vibration of nanobeams with intermediate support using nonlocal strain gradient theory. J Struct Eng Appl Mech2022; 5(2): 50–61.
WangCMZhangYYHeXQ. Vibration of nonlocal Timoshenko beams. Nanotechnol2007; 18: 1–9.
38.
LuLGuoXZhaoJ. Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory. Int J Eng Sci2017; 116: 12–24.
39.
KarkonM. An efficient finite element formulation for bending, free vibration and stability analysis of Timoshenko beams. J Braz Soc Mech Sci Eng2018; 40: 497.
40.
KocatürkTŞimşekM. Free vibration analysis of Timoshenko beams under various boundary conditions. Sigma J Eng Nat Sci2005; 30: 1–44.
41.
LeeJSchultzWW. Eigenvalue analysis of Timoshenko beams and axisymmetric mindlin plates by the pseudospectral method. J Sound Vib2004; 269: 609–621.
42.
LeeSJParkKS. Vibrations of Timoshenko beams with isogeometric approach. Appl Math Model2013; 37: 9174–9190.
43.
ZhangYSahmaniSYangZ, et al. Nonlocal and couple stress tensors in three-dimensional nonlinear dynamical stability behavior of microshells manufactured by smart materials. Acta Mech2022; 233: 5377–5401.
44.
SahmaniSSafaeiB. Nonlinear three-dimensional oscillations of probabilistic reinforced nanocomposite shells at microscale via modified strain gradient meshfree formulations. Proc IMechE, Part C: J Mechanical Engineering Science2023; 237(13): 3020–3034.
45.
Atif ShahzadMSahmaniSSafaeiB. Nonlocal couple stress-based meshless collocation model for nonlinear dynamic performance of microbeam-type piezoelectric energy harvesters. Eur J Mech Solids2023; 101: 1–20.
46.
AlshenawyRSahmaniSSafaeiB, et al. Surface stress effect on nonlinear dynamical performance of nanobeam-type piezoelectric energy harvesters via meshless collocation technique. Eng Anal Bound Elem2023; 152: 104–119.
47.
FaghidianSAŻurKKPanE. Stationary variational principle of mixture unified gradient elasticity. Int J Eng Sci2023; 182: 1–20.
48.
FaghidianSAŻurKKElishakoffI. Nonlinear flexure mechanics of mixture unified gradient nanobeams. Commun Nonlinear Sci Numer Simul2023; 117: 1–14.
49.
PapageorgiouDGLiZLiuM, et al. Mechanisms of mechanical reinforcement by graphene and carbon nanotubes in polymer nanocomposites. Nanoscale2020; 12: 2228–2267.
50.
PanN. The elastic constants of randomly oriented fiber composites: a new approach to prediction. Sci Eng Compos Mater1996; 5(2): 63–72.
51.
FanFLeiBSahmaniS, et al. On the surface elastic-based shear buckling characteristics of functionally graded composite skew nanoplates. Thin-Walled Struct2020; 154: 1–13.
52.
Ali FaghidianS. Analytical Approach for inverse reconstruction of eigenstrains and residual stresses in autofrettaged spherical pressure vessels. ASME J Press Vessel Technol2017; 139(4): 041202.
53.
SahmaniSFattahiAMAhmedNA. Surface elastic shell model for nonlinear primary resonant dynamics of FG porous nanoshells incorporating modal interactions. Int J Mech Sci2020; 165: 1–16.
54.
SarafrazASahmaniSAghdamMM. Nonlinear primary resonance analysis of nanoshells including vibrational mode interactions based on the surface elasticity theory. Appl Math Mech -Engl Ed2020; 41(2): 233–260.
55.
Kamil ŻurKFaghidianSA. Analytical and meshless numerical approaches to unified gradient elasticity theory. Eng Anal Bound Elem2021; 130: 238–248.
56.
SarafrazASahmaniSAghdamMM. Nonlinear secondary resonance of nanobeams under subharmonic and superharmonic excitations including surface free energy effects. Appl Math Model2019; 66: 195–226.
57.
YiHSahmaniSSafaeiB. On size-dependent large-amplitude free oscillations of FGPM nanoshells incorporating vibrational mode interactions. Arch Civil Mech Eng2020; 20: 48.
58.
ArdaMAydogduM. A Ritz formulation for vibration analysis of axially functionally graded Timoshenko-Ehrenfest beams. J Comput Appl Mech2022; 53(1): 102–115.
59.
BeheraLChakravertyS. Static analysis of nanobeams using Rayleigh–Ritz method. J Mech Mater Struct2017; 12(5): 603–616.
