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http://dx.doi.org/10.12989/scs.2022.42.5.699

Axial frequency analysis of axially functionally graded Love-Bishop nanorods using surface elasticity theory  

Nazemnezhad, Reza (School of Engineering, Damghan University)
Shokrollahi, Hassan (Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University)
Publication Information
Steel and Composite Structures / v.42, no.5, 2022 , pp. 699-710 More about this Journal
Abstract
This work presents a comprehensive study on the surface energy effect on the axial frequency analyses of AFGM nanorods in cylindrical coordinates. The AFGM nanorods are considered to be thin, relatively thick, and thick. In thin nanorods, effects of the inertia of lateral motions and the shear stiffness are ignored; in relatively thick nanorods, only the first one is considered; and in thick nanorods, both of them are considered in the kinetic energy and the strain energy of the nanorod, respectively. The surface elasticity theory which includes three surface parameters called surface density, surface stress, and surface Lame constants, is implemented to consider the size effect. The power-law form is considered for variation of the material properties through the axial direction. Hamilton's principle is used to derive the governing equations and boundary conditions. Due to considering the surface stress, the governing equation and boundary condition become inhomogeneous. After homogenization of them using an appropriate change of variable, axial natural frequencies are calculated implementing harmonic differential quadrature (HDQ) method. Comprehensive results including effects of geometric parameters and various material properties are presented for a wide range of boundary condition types. It is believed that this study is a comprehensive one that can help posterities for design and manufacturing of nano-electro-mechanical systems.
Keywords
free axial vibration; functionally graded materials; harmonic differential quadrature method; nanorod; surface energy;
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1 Akgoz, B. and Civalek, O . (2013), "Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory", Compos. Struct., 98, 314-322. https://doi.org/10.1016/j.compstruct.2012.11.020.   DOI
2 Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Advances Nano Res., 6(3), 257. http://dx.doi.org/10.12989/anr.2018.6.3.257.   DOI
3 Eremeyev, V.A., Rosi, G. and Naili, S. (2020), "Transverse surface waves on a cylindrical surface with coating", Int. J. Eng. Sci., 147, 103188. https://doi.org/10.1016/j.ijengsci.2019.103188.   DOI
4 Ghayesh, M.H. (2019d), " Viscoelastic dynamics of axially FG microbeams", Int. J. Eng. Sci., 135, 75-85. https://doi.org/10.1016/j.ijengsci.2018.10.005.   DOI
5 Nazemnezhad, R. and Kamali, K. (2018), "Free axial vibration analysis of axially functionally graded thick nanorods using nonlocal Bishop's theory", Steel Compos. Struct., 28(6), 749-758. https://doi.org/10.12989/scs.2018.28.6.749.   DOI
6 Nazemnezhad, R., Salimi, M., Hashemi, S.H. and Sharabiani, P.A. (2012), "An analytical study on the nonlinear free vibration of nanoscale beams incorporating surface density effects", Compos. Part B-Eng., 43(8), 2893-2897. https://doi.org/10.1016/j.compositesb.2012.07.029.   DOI
7 Zheng, S., Chen, D. and Wang, H. (2019), "Size dependent nonlinear free vibration of axially functionally graded tapered microbeams using finite element method", Thin Wall. Struct., 139, 46-52. https://doi.org/10.1016/j.tws.2019.02.033.   DOI
8 Nazemnezhad, R. and Hosseini-Hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199. https://doi.org/10.1016/j.compstruct.2013.12.006.   DOI
9 Xie, K., Wang, Y. and Fu, T. (2019), "Dynamic response of axially functionally graded beam with longitudinal-transverse coupling effect", Aerosp. Sci. Technol., 85, 85-95. https://doi.org/10.1016/j.ast.2018.12.004.   DOI
10 Zarezadeh, E., Hosseini, V. and Hadi, A. (2020), "Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory", Mech. Based Des. Struc., 48(4), 480-495. https://doi.org/10.1080/15397734.2019.1642766.   DOI
11 Watanabe, Y., Inaguma, Y., Sato, H. and Miura-Fujiwara, E. (2009), "A novel fabrication method for functionally graded materials under centrifugal force: The centrifugal mixed-powder method", Materials, 2(4), 2510-2525. https://doi.org/10.3390/ma2042510.   DOI
12 Ghayesh, M.H. (2018a), "Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams", Appl. Math. Model., 59, 583-596. https://doi.org/10.1016/j.apm.2018.02.017.   DOI
13 Patil, A.V., Beker, A.F., Wiertz, F.G., Heering, H.A., Coslovich, G., Vlijm, R. and Oosterkamp, T.H. (2010), "Fabrication and characterization of polymer insulated carbon nanotube modified electrochemical nanoprobes", Nanoscale, 2(5), 734-738. https://doi.org/10.1039/B9NR00281B.   DOI
14 Hosseini-Hashemi, S., Bedroud, M. and Nazemnezhad, R. (2013), "An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity", Compos. Struct., 103, 108-118. https://doi.org/10.1016/j.compstruct.2013.02.022.   DOI
15 Aal, A.A., El-Sheikh, S. and Ahmed, Y. (2009), "Electrodeposited composite coating of Ni-W-P with nano-sized rod-and spherical-shaped SiC particles", Mater. Res. Bull., 44(1), 151-159. https://doi.org/10.1016/j.materresbull.2008.03.008.   DOI
16 Akgoz, B. and Civalek, O . (2013), "Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)", Compos. Part B-Eng., 55, 263-268. https://doi.org/10.1016/j.compositesb.2013.06.035.   DOI
17 Ashok, C. and Rao, K.V. (2014), "ZnO/TiO2 nanocomposite rods synthesized by microwave-assisted method for humidity sensor application", Superlattice. Microst., 76, 46-54. https://doi.org/10.1016/j.spmi.2014.09.029.   DOI
18 Civalek, O. (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struct., 26(2), 171-186. https://doi.org/10.1016/j.engstruct.2003.09.005.   DOI
19 Nazemnezhad, R. and Shokrollahi, H. (2019), "Free axial vibration analysis of functionally graded nanorods using surface elasticity theory", Modares Mech. Eng., 18(9), 131-141.
20 Nazemnezhad, R. and Shokrollahi, H. (2020), "Free axial vibration of cracked axially functionally graded nanoscale rods incorporating surface effect", Steel Compos. Struct., 35(3), 449-462. http://dx.doi.org/10.12989/scs.2020.35.3.449.   DOI
21 Rajasekaran, S. and Bakhshi Khaniki, H. (2019), "Finite element static and dynamic analysis of axially functionally graded nonuniform small-scale beams based on nonlocal strain gradient theory", Mech. Adv. Mater. Struc., 26(14), 1245-1259. https://doi.org/10.1080/15376494.2018.1432797.   DOI
22 Zhang, T., Kumari, L., Du, G.H., Li, W.Z., Wang, Q.W., Balani, K. and Agarwal, A. (2009), "Mechanical properties of carbon nanotube-alumina nanocomposites synthesized by chemical vapor deposition and spark plasma sintering", Compos. Part A-Appl. S., 40(1), 86-93. https://doi.org/10.1016/j.compositesa.2008.10.003.   DOI
23 Shahba, A. and Rajasekaran, S. (2012), "Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials", Appl. Math. Model., 36(7), 3094-3111. https://doi.org/10.1016/j.apm.2011.09.073.   DOI
24 Wang, H., Liu, C. and Ding, H. (2009), "Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders", Acta Mech. Sinica, 25(4), 555-563. https://doi.org/10.1007/s10409-009-0251-9.   DOI
25 Yayli, M.O . (2018), "Free longitudinal vibration of a nanorod with elastic spring boundary conditions made of functionally graded material", Micro Nano Lett., 13(7), 1031-1035. https://doi.org/10.1049/mnl.2018.0181.   DOI
26 Ghayesh, M.H. (2019e), " Mechanics of viscoelastic functionally graded microcantilevers", Eur. J. Mech. A-Solid, 73, 492-499. https://doi.org/10.1016/j.euromechsol.2018.09.001.   DOI
27 Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. An., 57(4), 291-323. https://doi.org/10.1007/BF00261375.   DOI
28 Ghayesh, M.H. (2019a), "Nonlinear oscillations of FG cantilevers", Appl. Acoust., 145, 393-398. https://doi.org/10.1016/j.apacoust.2018.08.014.   DOI
29 Ebrahimi, F. and Barati, M.R. (2017), "Through-the-length temperature distribution effects on thermal vibration analysis of nonlocal strain-gradient axially graded nanobeams subjected to nonuniform magnetic field", J. Therm. Stresses, 40(5), 548-563. https://doi.org/10.1080/01495739.2016.1254076.   DOI
30 Rao, S.S. (2007), Vibration of Continuous Systems, Wiley Online Library.
31 Sinir, S., Cevik, M. and Sinir, B.G. (2018), "Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section", Compos. Part B-Eng., 148, 123-131. https://doi.org/10.1016/j.compositesb.2018.04.061.   DOI
32 Zeighampour, H. and Beni, Y.T. (2015), "Free vibration analysis of axially functionally graded nanobeam with radius varies along the length based on strain gradient theory", Appl. Math. Model., 39(18), 5354-5369. https://doi.org/10.1016/j.apm.2015.01.015.   DOI
33 Ghayesh, M.H. (2019b), " Viscoelastic mechanics of Timoshenko functionally graded imperfect microbeams", Compos. Struct., 225, 110974. https://doi.org/10.1016/j.compstruct.2019.110974.   DOI
34 Ghayesh, M.H. (2019c), "Asymmetric viscoelastic nonlinear vibrations of imperfect AFG beams", Appl. Acoust., 154, 121-128. https://doi.org/10.1016/j.apacoust.2019.03.022.   DOI
35 Ghayesh, M.H. (2018b), "Nonlinear Vibrations of Axially Functionally Graded Timoshenko Tapered Beams", J. Comput. Nonlin. Dyn., 13, 041002-1. https://doi.org/10.1115/1.4039191.   DOI
36 Zheng, Y., Wang, S., You, M., Tan, H. and Xiong, W. (2005), "Fabrication of nanocomposite Ti (C, N)-based cermet by spark plasma sintering", Mater. Chem. Phys., 92(1), 64-70. https://doi.org/10.1016/j.matchemphys.2004.12.031.   DOI
37 Hosseini-Hashemi, S. and Nazemnezhad, R. (2013), "An analytical study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects", Compos. Part B-Eng., 52, 199-206. https://doi.org/10.1016/j.compositesb.2013.04.023.   DOI
38 Nazemnezhad, R. and Fahimi, P. (2017), "Free torsional vibration of cracked nanobeams incorporating surface energy effects", Appl. Math. Mech.-Engl., 38(2), 217-230. https://doi.org/10.1007/s10483-017-2167-9.   DOI
39 Simsek, M. (2012), "Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods", Comp. Mater. Sci., 61, 257-265. https://doi.org/10.1016/j.commatsci.2012.04.001.   DOI