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http://dx.doi.org/10.12989/anr.2022.12.2.167

A hybrid conventional computer simulation via GDQEM and Newmark-beta techniques for dynamic modeling of a rotating micro nth-order system  

Fan, Linyuan (College of Mathematics and Data Science (College of Software), Minjiang University)
Zhang, Xu (Information Technology Center, Jingchu Institute of Technology)
Zhao, Xiaoyang (Birmingham City University, School of Computing and Digital Technology)
Publication Information
Advances in nano research / v.12, no.2, 2022 , pp. 167-183 More about this Journal
Abstract
In this paper, the free and forced vibration analysis of rotating cantilever nanoscale cylindrical beams and tubes is investigated under the external dynamic load to examine the nonlocal effect. A couple of nonlocal strain gradient theories with different beams and tubes theories, involving the Euler-Bernoulli, Timoshenko, Reddy beam theory along with the higher-order tube theory, are assumed to the mathematic model of governing equations employing the Hamilton principle in order to derive the nonlocal governing equations related to the local and accurate nonlocal boundary conditions. The two-dimensional functional graded material (2D-FGM), made by the axially functionally graded (AFG) in conjunction with the porosity distribution in the radial direction, is considered material modeling. Finally, the derived Partial Differential Equations (PDE) are solved via a couple of the generalized differential quadrature element methods (GDQEM) with the Newmark-beta techniques for the time-dependent results. It is indicated that the boundary conditions equations play a crucial task in responding to nonlocal effects for the cantilever structures.
Keywords
beam theory; bending vibration; forced vibration; rotating; time dependent analysis; tube theory;
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Times Cited By KSCI : 30  (Citation Analysis)
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89 Shafiei, N. and Kazemi, M. (2017b), "Nonlinear buckling of functionally graded nano-/micro-scaled porous beams", Compos. Struct., 178, 483-492. https://doi.org/10.1016/j.compstruct.2017.07.045.   DOI
90 Shafiei, N., Hamisi, M. and Ghadiri, M. (2020), "Vibration analysis of rotary tapered axially functionally graded Timoshenko nanobeam in thermal environment", J. Solid Mech., 12(1), 16-32.
91 Shi, X., Li, J. and Habibi, M. (2020), "On the statics and dynamics of an electro-thermo-mechanically porous GPLRC nanoshell conveying fluid flow", Mech. Based Des. Struct., 1-37. https://doi.org/10.1080/15397734.2020.1772088.   DOI
92 Wang, X. and Gu, H. (1997), "Static analysis of frame structures by the differential quadrature element method", Int. J. Numer. Method Eng., 40(4), 759-772. https://doi.org/10.1002/(SICI)1097-0207(19970228)40:4<759::AID-NME87>3.0.CO,2-9.   DOI
93 Abouelregal, A.E., Ahmad, H., Gepreeld, K.A. and Thounthong, P. (2021), "Modelling of vibrations of rotating nanoscale beams surrounded by a magnetic field and subjected to a harmonic thermal field using a state-space approach", Eur. Phys. J. Plus, 136(3), 268. http://doi.org/10.1140/epjp/s13360-021-01257-7.   DOI
94 Akbas, S.D. (2018a), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 6(3), 219-242. http://doi.org/10.12989/anr.2018.6.3.219.   DOI
95 Akbas, S.D. (2018b), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39-55. http://doi.org/10.12989/anr.2018.6.1.039.   DOI
96 Feng, Y., Zhang, B., Liu, Y., Niu, Z., Dai, B., Fan, Y. and Chen, X. (2021), "A 200-225-GHz manifold-coupled multiplexer utilizing metal waveguides", IEEE T. Microw. Theory., 69(12), 5327-5333. https://doi.org/10.1109/TMTT.2021.3119316.   DOI
97 Ghadiri, M., Shafiei, N. and Babaei, R. (2017d), "Vibration of a rotary FG plate with consideration of thermal and Coriolis effects", Steel. Compos. Struct., 25(2), 197-207. https://doi.org/10.12989/scs.2017.25.2.197.   DOI
98 Shafiei, N., Kazemi, M. and Ghadiri, M. (2016a), "Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler-Bernoulli microbeams", Physica E, 83, 74-87. https://doi.org/10.1016/j.physe.2016.04.011.   DOI
99 Shafiei, N., Kazemi, M. and Ghadiri, M. (2016c), "Nonlinear vibration of axially functionally graded tapered microbeams", Int. J. Eng. Sci., 102, 12-26. https://doi.org/10.1016/j.ijengsci.2016.02.007.   DOI
100 Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., 6(3), 279-298. http://doi.org/10.12989/anr.2018.6.3.279.   DOI
101 Xu, X.J., Deng, Z.C., Zhang, K. and Xu, W. (2016), "Observations of the softening phenomena in the nonlocal cantilever beams", Compos. Struct., 145, 43-57. https://doi.org/10.1016/j.compstruct.2016.02.073.   DOI
102 Yesilce, Y. (2011), "DTM and DQEM for free vibration of axially loaded and semi-rigid-connected Reddy-Bickford beam", Int. J. Numer. Method Biomed. Eng., 27(5), 666-693. https://doi.org/10.1002/cnm.1313.   DOI
103 Wang, Z., Yu, S., Xiao, Z. and Habibi, M. (2020), "Frequency and buckling responses of a high-speed rotating fiber metal laminated cantilevered microdisk", Mech. Adv. Mater. Struct., 1-14. https://doi.org/10.1080/15376494.2020.1824284.   DOI
104 Ding, H., Bao, X., Jamili-Shirvan, Z., Jin, J., Deng, L., Yao, K., Gong, P. and Wang, X. (2021), "Enhancing strength-ductility synergy in an ex situ Zr-based metallic glass composite via nanocrystal formation within high-entropy alloy particles", Mater. Des., 210, 110108. https://doi.org/10.1016/j.matdes.2021.110108.   DOI
105 Ebrahimi, F. and Dabbagh, A. (2018), "Wave dispersion characteristics of rotating heterogeneous magneto-electro-elastic nanobeams based on nonlocal strain gradient elasticity theory", J. Electromagnet. Wave., 32(2), 138-169. https://doi.org/10.1080/09205071.2017.1369903.   DOI
106 Atanasov, M.S. and Stojanovic, V. (2020), "Nonlocal forced vibrations of rotating cantilever nano-beams", Eur. J. Mech. A Solid., 79, 103850. https://doi.org/10.1016/j.euromechsol.2019.103850.   DOI
107 Singh, D.K. and Pal, P. (2021), "Forced Vibration Analysis of Stiffened Lock Gate Structure", J. Sound Vib., 510, 116278. https://doi.org/10.1016/j.jsv.2021.116278.   DOI
108 Van Vinh, P. and Tounsi, A. (2021), "The role of spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates", Eng. Comput., 1-19. https://doi.org/10.1007/s00366-021-01475-8.   DOI
109 Shafiei, N., Kazemi, M. and Ghadiri, M. (2016b), "Nonlinear vibration behavior of a rotating nanobeam under thermal stress using Eringen's nonlocal elasticity and DQM", Appl. Phys. A, 122(8), 728. https://doi.org/10.1007/s00339-016-0245-y.   DOI
110 Najaafi, N., Jamali, M., Habibi, M., Sadeghi, S., Jung, D.w. and Nabipour, N. (2021), "Dynamic instability responses of the substructure living biological cells in the cytoplasm environment using stress-strain size-dependent theory", J. Biomol. Struct. Dyn., 39(7), 2543-2554. https://doi.org/10.1080/07391102.2020.1751297.   DOI
111 Shafiei, N., Ghadiri, M., Makvandi, H. and Hosseini, S.A. (2017a), "Vibration analysis of Nano-Rotor's Blade applying Eringen nonlocal elasticity and generalized differential quadrature method", Appl. Math. Model., 43, 191-206. https://doi.org/10.1016/j.apm.2016.10.061.   DOI
112 Liu, Y., Wang, W., He, T., Moradi, Z. and Larco Benitez, M.A. (2021), "On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-021-01454-z.   DOI
113 Ghadiri, M., Shafiei, N. and Safarpour, H. (2017e), "Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen's nonlocal elasticity", Microsyst. Technol., 23(4), 1045-1065. https://doi.org/10.1007/s00542-016-2822-6.   DOI
114 Guo, S., He, Y., Liu, D., Lei, J. and Li, Z. (2018), "Dynamic transverse vibration characteristics and vibro-buckling analyses of axially moving and rotating nanobeams based on nonlocal strain gradient theory", Microsyst. Technol., 24(2), 963-977. https://doi.org/10.1007/s00542-017-3441-6.   DOI
115 Guo, Y., Mi, H. and Habibi, M. (2021), "Electromechanical energy absorption, resonance frequency, and low-velocity impact analysis of the piezoelectric doubly curved system", Mech. Syst. Signal Pr., 157, 107723. https://doi.org/10.1016/j.ymssp.2021.107723.   DOI
116 Habibi, M., Darabi, R., Sa, J.C.D. and Reis, A. (2021), "An innovation in finite element simulation via crystal plasticity assessment of grain morphology effect on sheet metal formability", 235(8), 1937-1951. https://doi.org/10.1177/14644207211024686.   DOI
117 Shafiei, N., Kazemi, M., Safi, M. and Ghadiri, M. (2016e), "Nonlinear vibration of axially functionally graded non-uniform nanobeams", Int. J. Eng. Sci., 106, 77-94. https://doi.org/10.1016/j.ijengsci.2016.05.009.   DOI
118 Shafiei, N., Mousavi, A. and Ghadiri, M. (2016f), "On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams", Int. J. Eng. Sci., 106, 42-56. https://doi.org/10.1016/j.ijengsci.2016.05.007.   DOI
119 Shafiei, N., Kazemi, M. and Fatahi, L. (2017b), "Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method", Mech. Adv. Mater. Struct., 24(3), 240-252. https://doi.org/10.1080/15376494.2015.1128025.   DOI
120 Shafiei, N. and Kazemi, M. (2017a), "Buckling analysis on the bi-dimensional functionally graded porous tapered nano-/micro-scale beams", Aerosp. Sci. Technol., 66, 1-11. https://doi.org/10.1016/j.ast.2017.02.019.   DOI
121 Shafiei, N., Ghadiri, M. and Mahinzare, M. (2019), "Flapwise bending vibration analysis of rotary tapered functionally graded nanobeam in thermal environment", Mech. Adv. Mater. Struct., 26(2), 139-155. https://doi.org/10.1080/15376494.2017.1365982.   DOI
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124 Pouretemad, A., Torabi, K. and Afshari, H. (2019b), "Free vibration analysis of a rotating non-uniform nanocantilever carrying arbitrary concentrated masses based on the nonlocal Timoshenko beam using DQEM", INAE Lett., 4(1), 45-58. https://doi.org/10.1007/s41403-019-00065-x.   DOI
125 Pradhan, S.C. and Murmu, T. (2010), "Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever", Physica E, 42(7), 1944-1949. https://doi.org/10.1016/j.physe.2010.03.004.   DOI
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128 Safarpour, H. and Ghadiri, M. (2017), "Critical rotational speed, critical velocity of fluid flow and free vibration analysis of a spinning SWCNT conveying viscous fluid", Microfluid. Nanofluid., 21(2), 22. https://doi.org/10.1007/s10404-017-1858-y.   DOI
129 Arefi, M. and Zenkour, A.M. (2018), "Free vibration analysis of a three-layered microbeam based on strain gradient theory and three-unknown shear and normal deformation theory", Steel. Compos. Struct., 26(4), 421-437. https://doi.org/10.12989/scs.2018.26.4.421.   DOI
130 Li, Y., Li, S., Guo, K., Fang, X. and Habibi, M. (2020b), "On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-020-01166-w.   DOI
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134 Shafiei, N., Mousavi, A. and Ghadiri, M. (2016g), "Vibration behavior of a rotating non-uniform FG microbeam based on the modified couple stress theory and GDQEM", Compos. Struct., 149, 157-169. https://doi.org/10.1016/j.compstruct.2016.04.024.   DOI
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136 Liu, Z., Su, S., Xi, D. and Habibi, M. (2020a), "Vibrational responses of a MHC viscoelastic thick annular plate in thermal environment using GDQ method", Mech. Based Des. Struct., 1-26. https://doi.org/10.1080/15397734.2020.1784201.   DOI
137 Liu, Z., Wu, X., Yu, M. and Habibi, M. (2020b), "Large-amplitude dynamical behavior of multilayer graphene platelets reinforced nanocomposite annular plate under thermo-mechanical loadings", Mech. Based Des. Struct., 1-25. https://doi.org/10.1080/15397734.2020.1815544.   DOI
138 Al-Furjan, M.S.H., Dehini, R., Khorami, M., Habibi, M. and won Jung, D. (2021a), "On the dynamics of the ultra-fast rotating cantilever orthotropic piezoelectric nanodisk based on nonlocal strain gradient theory", Compos. Struct., 255, 112990. https://doi.org/10.1016/j.compstruct.2020.112990.   DOI
139 Al-Furjan, M.S.H., Fereidouni, M., Sedghiyan, D., Habibi, M. and Jung, D.w. (2021b), "Three-dimensional frequency response of the CNT-Carbon-Fiber reinforced laminated circular/annular plates under initially stresses", Compos. Struct., 257, 113146. https://doi.org/10.1016/j.compstruct.2020.113146.   DOI
140 Talebitooti, R., Rezazadeh, S.O. and Amiri, A. (2019), "Comprehensive semi-analytical vibration analysis of rotating tapered AFG nanobeams based on nonlocal elasticity theory considering various boundary conditions via differential transformation method", Compos. Part B Eng., 160, 412-435. https://doi.org/10.1016/j.compositesb.2018.12.085.   DOI
141 Mirjavadi, S.S., Matin, A., Shafiei, N., Rabby, S. and Mohasel Afshari, B. (2017b), "Thermal buckling behavior of two-dimensional imperfect functionally graded microscale-tapered porous beam", J. Therm. Stress., 40(10), 1201-1214. https://doi.org/10.1080/01495739.2017.1332962.   DOI
142 Mirjavadi, S.S., Mohasel Afshari, B., Shafiei, N., Rabby, S. and Kazemi, M. (2017c), "Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam", J. Vib. Control, 24(18), 4211-4225. https://doi.org/10.1177/1077546317721871.   DOI
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148 Ma, L., Liu, X. and Moradi, Z. (2021), "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. Comput., 1-25. https://doi.org/10.1007/s00366-020-01210-9.   DOI
149 Al-Furjan, M.S.H., Habibi, M., Ni, J., Jung, D.W. and Tounsi, A. (2020a), "Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-020-01200-x.   DOI
150 Al-Furjan, M.S.H., Habibi, M., Ghabussi, A., Safarpour, H., Safarpour, M. and Tounsi, A. (2021c), "Non-polynomial framework for stress and strain response of the FG-GPLRC disk using three-dimensional refined higher-order theory", Eng. Struct., 228, 111496. https://doi.org/10.1016/j.engstruct.2020.111496.   DOI
151 Al-Furjan, M.S.H., Safarpour, H., Habibi, M., Safarpour, M. and Tounsi, A. (2020c), "A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-020-01088-7.   DOI
152 Al-Furjan, M.S.H., Habibi, M., rahimi, A., Chen, G., Safarpour, H., Safarpour, M. and Tounsi, A. (2020b), "Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM", Eng. Comput., 1-24. https://doi.org/10.1007/s00366-020-01144-2.   DOI
153 Shafiei, N., Mirjavadi, S.S., MohaselAfshari, B., Rabby, S. and Kazemi, M. (2017d), "Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Method Appl. Mech. Eng., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007.   DOI
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