Analysis of Nonlinear Vibrations of Slightly Curved Tripled-Walled Carbon Nanotubes Resting on Elastic Foundations in a Magneto-Thermal Environment
الموضوعات :M.G Sobamowo 1 , J.O Akanmu 2 , O.A Adeleye 3 , A.A Yinusa 4
1 - Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria
2 - Department of Civil and Environmental Engineering, University of Lagos, Akoka, Lagos, Nigeria
3 - Department of System Engineering, University of Lagos, Akoka, Lagos, Nigeria
4 - Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria
الکلمات المفتاحية: Multi-walled carbon nanotubes, Nonlocal elastic theory, Magnetic and thermal environment, Winkler and Pasternak foundations, Small-scale effects,
ملخص المقالة :
In this work, nonlocal elasticity theory is applied to analyze nonlinear free vibrations of slightly curved multi-walled carbon nanotubes resting on nonlinear Winkler and Pasternak foundations in a thermal and magnetic environment. With the aid of Galerkin decomposition method, the systems of nonlinear partial differential equations are transformed into systems of nonlinear ordinary differential equations which are solved using homotopy perturbation method. The influences of elastic foundations, magnetic field, temperature rise, interlayer forces, small scale parameter and boundary conditions on the frequency ratio are investigated. It is observed form the results that the frequency ratio for all boundary conditions decreases as the number of walls increases. Also, it is established that the frequency ratio is highest for clamped-simple supported and lowest for clamped-clamped supported. Further investigations on the controlling parameters of the phenomena reveal that the frequency ratio decreases with increase in the value of spring constant (k1) temperature and magnetic field strength. It is hoped that this work will enhance the applications of carbon nanotubes in structural, electrical, mechanical and biological applications especially in a thermal and magnetic environment.
[1] Iijima S., 1991, Helical micro tubes of graphitic carbon, Nature 354: 56-58.
[2] Terrones M., Banhart F., Grobert N., Charlier J., Terrones C., Ajayan H., 2002, Molecular junctions by joining single-walled carbon nanotubes, Physical Review Letters 89: 07550.
[3] Nagy P., Ehlich R., Biro L.P., Gjyulai J., 2000, Y-branching of single walled carbon nanotubes, Applied Physics A 70: 481-483.
[4] Chernozatonskii L.A., 1992, Carbon nanotubes connectors and planar jungle gyms, Applied Physics A 172: 173-176.
[5] Liew K.M., Wong C.H., He X.Q., Tan M.J., Meguid S.A., 2004, Nanomechanics of single and multiwalled carbon nanotubes, Physical Review B 69: 115429.
[6] Pantano A., Boyce M.C., Parks D.M., 2004, Mechanics of axial compression of single and multi-wall carbon nanotubes, Journal of Engineering Materials and Technology 126: 279-284.
[7] Pantano A., Parks D.M., Boyce M.C., 2004, Mechanics of deformation of single- and multi-wall carbon nanotubes, Journal of the Mechanics and Physics of Solids 52: 789-821.
[8] Qian D., Wagner G.J., Liu W.K., Yu M.F., Ruoff R.S., 2002, Mechanics of carbon nanotubes, Applied Mechanics Reviews 55: 495-533.
[9] Salvetat J.P., Bonard J.-M., Thomson N.H., Kulik A.J., Forro L., Benoit W., Zuppiroli L., 1999, Mechanical properties of carbon nanotubes, Applied Physics A 69: 255-260.
[10] Sears A., Batra R.C., 2006, Buckling of carbon nanotubes under axial compression, Physical Review B 73: 1595220.
[11] Yoon J., Ru C.Q., Mioduchowski A., 2002, Noncoaxial resonance of an isolated multiwall carbon nanotube, Physical Review B 66: 233402.
[12] Wang X., Cai H., 2006, Effects of initial stress on non-coaxial resonance of multi-wall carbon nanotubes, Acta Materialia 54: 2067-2074.
[13] Wang C.M., Tan V.B.C., Zhang Y.Y., 2006, Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, Journal of Sound and Vibration 294: 1060-1072.
[14] Zhang Y., Liu G., Han X., 2005, Transverse vibrations of double-walled carbon nanotubes under compressive axial load, Physics Letters A 340: 258-266.
[15] Elishakoff I., Pentaras D., 2009, Fundamental natural frequencies of double-walled carbon nanotubes, Journal of Sound and Vibration 322: 652-664.
[16] Buks E., Yurke B., 2006, Mass detection with nonlinear nanomechanical resonator, Physical Review E 74: 046619.
[17] Postma H.W.C., Kozinsky I., Husain A., Roukes M.L., 2005, Dynamic range of nanotube- and nanowire-based electromechanical systems, Applied Physics Letters 86: 223105.
[18] Fu Y.M., Hong J.W., Wang X.Q., 2006, Analysis of nonlinear vibration for embedded carbon nanotubes, Journal of Sound and Vibration 296: 746-756.
[19] Xu K.Y., Guo X.N., Ru C.Q., 2006, Vibration of a double-walled carbon nanotube aroused by nonlinear intertube van der Waals forces, Journal of Applied Physics 99: 064303 .
[20] Dequesnes M., Tang Z., Aluru N.R., 2004, Static and dynamic analysis of carbon nanotube-based switches, Transactions of the ASME 126: 230-237.
[21] Ouakad H.M., Younis M.I., 2010, Nonlinear dynamics of electrically actuated carbon nanotube resonators, Journal of Computational and Nonlinear Dynamics 5: 011009.
[22] Zamanian M., Khadem S.E., Mahmoodi S.N., 2009, Analysis of non-linear vibrations of a microresonator under piezoelectric and electrostatic actuations, Journal of Mechanical Engineering Science 223: 329-344.
[23] Abdel-Rahman E.M., Nayfeh A.H., 2003, Secondary resonances of electrically actuated resonant microsensors, Journal of Micromechnics and Microengineering 13: 491-501.
[24] Hawwa M.A., Al-Qahtani H.M., 2010, Nonlinear oscillations of a double-walled carbon nanotube, Computational Materials Science 48: 140-143.
[25] Hajnayeb A., Khadem S.E., 2012, Nonlinear vibration and stability analysis of a double-walled carbon nanotube under electrostatic actuation, Journal of Sound and Vibration 331: 2443-2456.
[26] Belhadj A., Boukhalfa A., Belalia S., 2016, Carbon nanotube structure vibration based on non local elasticity, Journal of Modern Materials 3(1): 9-13.
[27] Lei X.W., Natsuki T., Shi J.X., Ni Q.Q., 2012, Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model, Composites Part B 43: 64-69.
[28] Sharabiani P.A., Yazdi M.R.H., 2013, Nonlinear free vibrations of functionally graded nanobeams with surface effects, Composites Part B 45: 581-586.
[29] Wang L., 2010, Vibration analysis of fluid-conveying nanotubes with consideration of surface effects, Physica E 43: 437-439.
[30] Biro L.P., Horvat Z.E., Mark G.I., Osvath Z., Koos A.A., Santucci S., Kenny J.M., 2004, Carbon nanotube Y junctions: growth and properties, Diamond and Related Materials 13: 241-249.
[31] Lin R.M., 2012, Nanoscale vibration characterization of multi-layered graphene sheets embedded in an elastic medium, Computational Materials Science 53: 44-52.
[32] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A 373: 1062-1069.
[33] Ghorbanpour A., Zarei M.S., Amir S., Khoddami M.Z., 2013, Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model, Physica B 410: 188-196.
[34] Ghorbanpour A., Amir S., 2013, Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory, Physica B 419: 1-6.
[35] Eichler A., Moser J., Chaste J., Zdrojek M., Wilson-Rae R.I., Bachtold A., 2011, Nonlinear damping in mechanical resonators made from carbon nanotubes and grapheme, Nature Nanotechnology 6: 339-342.
[36] Dodds H.L., Runyan H., 1965, Effects of high velocity fluid flow in the bending vibrations and static divergence of a simply supported pipe, National Aeronautical and Space Adminitration Report, NASA TN D-2870.
[37] Sobamowo M.G., 2017, Nonlinear thermal and flow induced vibration analysis of fluid-conveying carbon nanotube resting on Winkler and Pasternak foundations, Thermal Science and Engineering Progress 4: 133-149.
[38] Liu F., Wagterveld R.M., Gebben B., Otto M.J., Biesheuvel P.M., Hamelers H.V., 2014, Carbon nanotube yarns as strong flexible conductive capacitive electrodes, Colloid and Interface Science Communications 3: 9-12.
[39] Sobamowo M.G., Yinusa A.A., 2018, Thermo-fluidic parameters effects on nonlinear vibration of fluid-conveying nanotube resting on elastic foundations using Homotopy Perturbation method, Journal of Thermal Engineering 4(4): 2211-2233.
[40] Coşkun S.B., Atay M.T., Öztürk B., 2011, Transverse vibration analysis of Euler-Bernoulli beams using analytical approximate techniques, Advances in Vibration Analysis Research.
[41] Sobamowo M.G., Yinusa A.A., 2017, Power Series -After Treatment Technique for Nonlinear Cubic Duffing and Double-Well Duffing Oscillators, Journal of Computational Applied Mechanics 48(2): 297-306.
[42] Yoon J., Ru C.Q., Mioduchowski A., 2002, Non-coaxial resonance of an isolated multiwall carbon nanotube, Physical Review B 66: 233402-233414.
[43] Yoon J., Ru C.Q., Mioduchowski A., 2003,Vibration of an embedded multiwalled carbon nanotube [J], Composites Science and Technology 63: 1533-1542.
[44] Ansari R., Hemmatnezhad M., 2011, Nonlinear vibrations of embedded multi-walled carbon nanotubes using a variational approach, Mathematical and Computer Modelling 53(5-6): 927-938.
[45] Ghorbanpour Arani A., Rabbani H., Amir S., Khoddami Maraghi Z., Mohammadimehr M., Haghparast E., 2011, Analysis of nonlinear vibrations for multi-walled carbon nanotubes embedded in an elastic medium, Journal of Solid Mechanics 3(3): 258-270.
[46] Yoon J., Ru C.Q. Miodochowski A., 2003, Vibration of an embedded multiwalled carbon nanotubes, Composites Science and Technology 63:1533-1542.
[47] Fu Y.M., Hong J.W., Wang X.Q., 2006, Analysis of nonlinear vibration for embedded carbon nanotubes, Journal of Sound and Vibration 296: 746-756.
[48] Wang C.M., Tan V.B.C., Zhang Y.Y., 2006, Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, Journal of Sound and Vibration 294: 1060-1072.
[49] Aydogdu M., 2008, Vibration of multi-walled carbon nanotubes by generalized shear deformation theory, International Journal of Mechanical Sciences 50: 837-844.
[50] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface wave, Journal of Applied Physics 54(9): 4703-4710.
[51] Eringen A.C., 1972, Linear theory of nonlocal elasticity and dispersion of plane waves, International Journal of Engineering Science 10(5): 425-435.
[52] Eringen A.C., Edelen D.G.B., 1972, On nonlocal elasticity, International Journal of Engineering Science 10(3): 233-248.
[53] Eringen A.C., 2002, Nonlocal Continuum Field Theories, Springer, New York.
[54] Sobamowo M.G., 2016, Nonlinear vibration analysis of single-walled carbon nanotube conveying fluid in slip boundary conditions using variational iterative method, Journal of Applied and Computational Mechanics 2(4): 208-221.
[55] Arefi A., Nahvi H., 2017, Stability analysis of an embedded single-walled carbon nanotube with small initial curvature based on nonlocal theory, Mechanics of Advanced Materials and Structures 24: 962-970.
[56] Kitipornchai S., He X.Q., Liew K.M., 2005, Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix, Journal of Applied Physics 97: 114318.
[57] Sobamowo M.G., 2017, Nonlinear analysis of flow-induced vibration in fluid-conveying structures using differential transformation method with cosine-aftertreatment technique, Iranian Journal of Mechanical Engineering Transactions of the ISME 18(1): 5-42.
[58] Sobamowo M.G., 2017, Nonlinear thermal and flow-induced vibration analysis of fluid-conveying carbon nanotube resting on Winkler and Pasternak foundations,Thermal Science and Engineering Progress 4:133-149.
[59] Sobamowo M.G., Ogunmola B.Y., Osheku C.A., 2017, Thermo-mechanical nonlinear vibration analysis of fluid-conveying structures subjected to different boundary conditions using Galerkin-Newton-Harmonic balancing method, Journal of Applied and Computational Mechanics 3(1): 60-79.
[60] Pentaras D., Elishakoff I., 2011, Free vibration of triple-walled carbon nanotubes, Acta Mechanica 221: 239-249.
[61] Sobamowo M.G., Akinshilo A.T., 2018, Double diffusive magnetohydrodynamic squeezing flow of nanofluid between two parallel disks with slip and temperature jump boundary conditions, Applied and Computational Mechanics 11(2): 167-182.
[62] Sobamowo M.G., Adeleye O.A., 2018, Homotopy perturbation method for kinetic analysis of thermal inactivation of jack bean urease, Karbala International Journal of Modern Science 4: 187-199.
[63] Yinusa A.A., Sobamowo M.G., 2019, Analysis of dynamic behaviour of a tensioned carbon nanotube in thermal and pressurized environment, Karbala International Journal of Modern Science 5: 1-11.
