An Analytical Solution on Size Dependent Longitudinal Dynamic Response of SWCNT Under Axial Moving Harmonic Load

Subject Areas : Engineering

F  Khosravi ¹ (Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran)
M  Simyari ² (Department of Mechanical Engineering, University of Tehran, Tehran, Iran)
S. A  Hosseini ³ (Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran)
M  Ghadiri ⁴ (Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran)

Received: 2020-06-11 Accepted : 2020-08-12 Published : 2020-09-30

Keywords:

References:

Kroto H.W., 1985, C60: Buckminsterfullerene, Nature 318: 162-163.
[2] Krätschmer W., 1990, Solid C60: a new form of carbon, Nature 347: 354-358.
[3] Iijima S., 1991, Synthesis of Carbon Nanotubes, Nature 354: 56-58.
[4] Iijima S., Ichihashi T., 1993, Single-shell carbon nanotubes of 1-nm diameter, Nature 363: 603-605.
[5] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 56-58.
[6] Lu X., Chen Z., 2005, Curved pi-conjugation, aromaticity, and the related chemistry of small fullerenes (< C60) and single-walled carbon nanotubes, Chemical Reviews 105(10): 3643-3696.
[7] Dresselhaus M., 2004, Electronic, thermal and mechanical properties of carbon nanotubes. Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences 362: 2065-2098.
[8] Hong S., Myung S., 2007, Nanotube electronics: A flexible approach to mobility, Nature Nanotechnology 2(4): 207-208.
[9] Bethune D., 1993, Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls, Nature 363: 605-607.
[10] Dai H., 2002, Carbon nanotubes: opportunities and challenges, Surface Science 500 (1-3): 218-241.
[11] De Volder M.F., 2013, Carbon nanotubes: present and future commercial applications, Science 339: 535-539.
[12] Esawi A.M., Farag M.M., 2007, Carbon nanotube reinforced composites: potential and current challenges, Materials & Design 28(9): 2394-2401.
[13] Mubarak N., 2014, An overview on methods for the production of carbon nanotubes, Journal of Industrial and Engineering Chemistry 20(4): 1186-1197.
[14] Lei Z., Zhang L., Liew K., 2015, Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method, Composite Structures 127: 245-259.
[15] Zhang L., Song Z., Liew K., 2015, State-space Levy method for vibration analysis of FG-CNT composite plates subjected to in-plane loads based on higher-order shear deformation theory, Composite Structures 134: 989-1003.
[16] Natarajan S., Haboussi M., Manickam G., 2014, Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets, Composite Structures 113: 197-207.
[17] Wang Z.-X., Shen H.-S., 2012, Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets, Composites Part B: Engineering 43(2): 411-421.
[18] Ma J., 2010, Diameters of single-walled carbon nanotubes (SWCNTs) and related nanochemistry and nanobiology, Frontiers of Materials Science in China 4(1): 17-28.
[19] Sethuraman A., Stroscio M.A., Dutta M., 2004, Potential Applications of Carbon Nanotubes in Bioengineering, Springer.
[20] Chen Y., Zhang J., 2014, Chemical vapor deposition growth of single-walled carbon nanotubes with controlled structures for nanodevice applications, Accounts of Chemical Research 47(8): 2273-2281.
[21] Fukuda T., Arai F., Dong L., 2003, Assembly of nanodevices with carbon nanotubes through nanorobotic manipulations, Proceedings of the IEEE 91(11): 1803-1818.
[22] Ma P.-C., 2010, Dispersion and functionalization of carbon nanotubes for polymer-based nanocomposites: a review, Composites Part A: Applied Science and Manufacturing 41(10): 1345-1367.
[23] Sahoo N.G., 2010, Polymer nanocomposites based on functionalized carbon nanotubes, Progress in Polymer Science 35(7): 837-867.
[24] Zarepour M., Hosseini S.A., Ghadiri M., 2017, Free vibration investigation of nano mass sensor using differential transformation method, Applied Physics A 123(3): 181.
[25] Namvar M., 2017, Experimental and analytical investigations of vibrational behavior of U-shaped atomic force microscope probe considering thermal loading and the modified couple stress theory, The European Physical Journal Plus 132(6): 247.
[26] Sourki R., Hosseini S.A., 2017, Coupling effects of nonlocal and modified couple stress theories incorporating surface energy on analytical transverse vibration of a weakened nanobeam, The European Physical Journal Plus 132(4): 184.
[27] Refaeinejad V., Rahmani O., Hosseini S.A., 2017, Evaluation of nonlocal higher order shear deformation models for the vibrational analysis of functionally graded nanostructures, Mechanics of Advanced Materials and Structures 24(13): 1116-1123.
[28] Rahmani O., Hosseini S.A., Parhizkari M., 2017, Buckling of double functionally-graded nanobeam system under axial load based on nonlocal theory: an analytical approach, Microsystem Technologies 23(7): 2739-2751.
[29] Hayati H., Hosseini S.A., Rahmani O.,2016, Coupled twist–bending static and dynamic behavior of a curved single-walled carbon nanotube based on nonlocal theory, Microsystem Technologies 23: 2393-2401.
[30] Eringen A.C., Edelen D., 1972, On nonlocal elasticity, International Journal of Engineering Science 10(3): 233-248.
[31] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54(9): 4703-4710.
[32] Kahrobaiyan M., 2010, Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory, International Journal of Engineering Science 48(12): 1985-1994.
[33] Ansari R., 2015, Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model, Acta Mechanica Sinica 31(5): 708-719.
[34] Farajpour M.R., 2016, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, Micro & Nano Letters 11(6): 302-307.
[35] Behrouz S.J., Rahmani O., Hosseini S.A., 2019, On nonlinear forced vibration of nano cantilever-based biosensor via couple stress theory, Mechanical Systems and Signal Processing 128: 19-36.
[36] Hosseini S.A., Rahmani O., 2018, Modeling the size effect on the mechanical behavior of functionally graded curved micro/nanobeam, Thermal Science and Engineering 1(2): 1-20.
[37] Rahmani O., 2018, Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory, Steel and Composite Structures 27(3): 371-388.
[38] Rahmani O., 2018, Free vibration of deep curved FG nano-beam based on modified couple stress theory, Steel and Composite Structures 26(5): 607-620.
[39] Rahmani O., 2018, Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory, The European Physical Journal Plus 133(2): 42.
[40] Ghadiri M., 2018, In-Plane and out of plane free vibration of U-shaped AFM probes based on the nonlocal elasticity, Journal of Solid Mechanics 10(2): 285-299.
[41] Hosseini S.A., Rahmani O., 2018, Bending and vibration analysis of curved FG nanobeams via nonlocal Timoshenko model, Smart Construction Research 2(2): 1-17.
[42] Xu K., Guo X., Ru C., 2006, Vibration of a double-walled carbon nanotube aroused by nonlinear intertube van der Waals forces, Journal of Applied Physics 99(6): 064303.
[43] Lee H.-L., Chang W.-J., 2009, Vibration analysis of a viscous-fluid-conveying single-walled carbon nanotube embedded in an elastic medium, Physica E: Low-Dimensional Systems and Nanostructures 41(4): 529-532.
[44] Moradi-Dastjerdi R., 2014, Vibration analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube based on mesh-free method, Journal of Composite Materials 48(15): 1901-1913.
[45] Pourseifi M., Rahmani O., Hoseini S.A., 2015, Active vibration control of nanotube structures under a moving nanoparticle based on the nonlocal continuum theories, Meccanica 50(5): 1351-1369.
[46] Mahdavi M., Jiang L., Sun X., 2011, Nonlinear vibration of a double-walled carbon nanotube embedded in a polymer matrix, Physica E: Low-Dimensional Systems and Nanostructures 43(10): 1813-1819.
[47] Kiani K., 2010, Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique, Physica E: Low-Dimensional Systems and Nanostructures 43(1): 387-397.
[48] Askari H., Esmailzadeh E., Zhang D., 2014, Nonlinear vibration analysis of nonlocal nanowires, Composites Part B: Engineering 67: 607-613.
[49] Ansari R., Torabi J., Shojaei M.F., 2017, Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading, Composites Part B: Engineering 109: 197-213.
[50] Yas M., Heshmati M., 2012, Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Applied Mathematical Modelling 36(4): 1371-1394.
[51] Şimşek M., 2010, Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory, Physica E: Low-Dimensional Systems and Nanostructures 43(1): 182-191.
[52] Malekzadeh P., Zarei A., 2014, Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers, Thin-Walled Structures 82: 221-232.
[53] Joshi A.Y., Harsha S., Sharma S.C., 2010, Vibration signature analysis of single walled carbon nanotube based nanomechanical sensors, Physica E: Low-Dimensional Systems and Nanostructures 42(8): 2115-2123.
[54] Aydogdu M., 2012, Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity, Mechanics Research Communications 43: 34-40.
[55] Aydogdu M., 2015, A nonlocal rod model for axial vibration of double-walled carbon nanotubes including axial van der Waals force effects, Journal of Vibration and Control 21(16): 3132-3154.
[56] Murmu T., Adhikari S., 2010, Nonlocal effects in the longitudinal vibration of double-nanorod systems, Physica E: Low-Dimensional Systems and Nanostructures 43(1): 415-422.
[57] Şimşek M., 2012, Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods, Computational Materials Science 61: 257-265.
[58] Murmu T., Adhikari S., 2011, Axial instability of double-nanobeam-systems, Physics Letters A 375(3): 601-608.
[59] Danesh M., Farajpour A., Mohammadi M., 2012, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications 39(1): 23-27.
[60] Filiz S., Aydogdu M., 2010, Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity, Computational Materials Science 49(3): 619-627.
[61] Mohammadian M., Abolbashari M.H., Hosseini S.M., 2019, Axial vibration of hetero-junction CNTs mass nanosensors by considering the effects of small scale and connecting region: An analytical solution, Physica B: Condensed Matter 553: 137-150.
[62] Liu K.-C., Friend J., Yeo L., 2009, The axial–torsional vibration of pretwisted beams, Journal of Sound and Vibration 321(1-2): 115-136.
[63] Aydogdu M., Filiz S., 2011, Modeling carbon nanotube-based mass sensors using axial vibration and nonlocal elasticity, Physica E: Low-Dimensional Systems and Nanostructures 43(6): 1229-1234.
[64] Bouadi A., 2018, A new nonlocal HSDT for analysis of stability of single layer graphene sheet, Advances in Nano Research 6(2): 147-162.
[65] Hamza-Cherif R., 2018, Vibration analysis of nano beam using differential transform method including thermal effect, Journal of Nano Research 54: 1-14.
[66] Kadari B., 2018, Buckling analysis of orthotropic nanoscale plates resting on elastic foundations, Journal of Nano Research 55: 42-56.
[67] Yazid M., 2018, A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium, Smart Structures and Systems 21(1): 15-25.
[68] Youcef D.O., 2018, Dynamic analysis of nanoscale beams including surface stress effects, Smart Structures and Systems 21(1): 65-74.
[69] Draoui A., 2019, Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT), Journal of Nano Research 57: 117-135.
[70] Mokhtar Y., 2018, A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory, Smart Structures and Systems 21(4): 397-405.
[71] Boutaleb S., 2019, Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT, Advances in Nano Research 7(3): 189-206.
[72] Karami B., 2018, A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates, Steel and Composite Structures 28(1): 99-110.
[73] Karami B., Janghorban M., Tounsi A.,2018, Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles, Steel and Composite Structures 27(2): 201-216.
[74] Karami B., Janghorban M., Tounsi A., 2018, Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory, Thin-Walled Structures 129: 251-264.
[75] Bellifa H., 2017, A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams, Structural Engineering and Mechanics 62(6): 695-702.
[76] Karami B., Janghorban M., Tounsi A., 2017, Effects of triaxial magnetic field on the anisotropic nanoplates, Steel and Composite Structures 25(3): 361-374.
[77] Bouafia K., 2017, A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams, Smart Structures and Systems 19(2): 115-126.
[78] Zemri A., 2015, A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory, Structural Engineering and Mechanics 54(4): 693-710.
[79] Şimşek M., 2011, Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle, Computational Materials Science 50(7): 2112-2123.