Axial vibration of double-walled carbon nanotubes using double-nanorod model with van der Waals force under Pasternak medium and magnetic effects
Author affiliations
DOI:
https://doi.org/10.15625/0866-7136/16582Keywords:
critical buckling of double-walled nanotube, differential transform method, Pasternak medium support, magentic force effectAbstract
The present study investigates the axial vibration of double-walled nanotubes. Using the nanorod continuum model with the van der Waals effect, the vibrational frequencies are studied. Aydogdu (Journal of Vibration and Control, Vol. 21, Issue 16, (2015), 3132-3154) proposed a reliable model for the study of axial vibration in a double-walled nanotube. This model provided a detailed investigation of axial vibration using van der Waals effects. But sometimes, the wrong equation might lead to erroneous scientific results. The incorrect term for axial vibration in the double-walled nanotube model is taken care of in the present study for the correct scientific inferences. Effectively, the axial vibrational frequencies appear without decoupling the continuum model as for primary and secondary nanotubes. The semi-analytical method estimates the axial vibrational frequencies of the double-walled nanotube as a coupled model. Two different boundary conditions like clamped-clamped and clamped-free support, are considered in this computation. The Pasternak medium support and magnetic effects influence the vibrational frequencies of the first and second nanotube for the first time. The Pasternak constant and magnetic parameters don't vary with the length of the nanotube for axial vibration. It means that still more understanding requires in modeling the Pasternak medium and magnetic force for the double-nanotube to model axial vibration.
Downloads
References
S. Iijima. Helical microtubules of graphitic carbon. Nature, 354, (6348), (1991), pp. 56–58.
M. Endo, S. Iijima, and M. S. Dresselhaus. Carbon nanotubes. Elsevier, (1996).
G. Dresselhaus, M. S. Dresselhaus, and R. Saito. Physical properties of carbon nanotubes. World Scientific, (1998).
I. Elishakoff, K. Dujat, G. Muscolino, S. Bucas, T. Natsuki, C. M. Wang, D. Pentaras, C. Versaci, J. Storch, N. Challamel, Y. Zhang, and G. Ghyselinck. Carbon nanotubes and nanosensors: Vibration, buckling and balistic impact. JohnWiley & Sons, (2013).
C. Hierold, O. Brand, G. K. Fedder, J. G. Korvink, and O. Tabata. Carbon nanotube devices: Properties, modeling, integration and applications. JohnWiley & Sons, (2008).
M. Aydogdu. Axial vibration of the nanorods with the nonlocal continuum rod model. Physica E: Low-dimensional Systems and Nanostructures, 41, (5), (2009), pp. 861–864.
K. Kiani. 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, (2010), pp. 387–397.
S. Narendar and S. Gopalakrishnan. Nonlocal scale effects on ultrasonic wave characteristics of nanorods. Physica E: Low-dimensional Systems and Nanostructures, 42, (2010), pp. 1601–1604.
M. Aydogdu. Longitudinal wave propagation in nanorods using a general nonlocal unimodal rod theory and calibration of nonlocal parameter with lattice dynamics. International Journal of Engineering Science, 56, (2012), pp. 17–28.
Z. M. Islam, P. Jia, and C. W. Lim. Torsional wave propagation and vibration of circular nanostructures based on nonlocal elasticity theory. International Journal of Applied Mechanics, 6, (02), (2014), pp. 1450011–1450027.
M. Aydogdu and U. Gul. Longitudinal vibration of double nanorod systems using doublet mechanics theory. Structural Engineering and Mechanics, 73, (2020), pp. 37–52.
L. Li, Y. Hu, and X. Li. Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory. International Journal of Mechanical Sciences, 115, (2016), pp. 135–144.
K. Kiani. Nonlocal-integro-differential modeling of vibration of elastically supported nanorods. Physica E: Low-dimensional Systems and Nanostructures, 83, (2016), pp. 151–163.
X. Zhu and L. Li. On longitudinal dynamics of nanorods. International Journal of Engineering Science, 120, (2017), pp. 129–145.
R. Nazemnezhad and K. Kamali. An analytical study on the size dependent longitudinal vibration analysis of thick nanorods. Materials Research Express, 5, (2018), pp. 075016–075028.
A. Farajpour, M. H. Ghayesh, and H. Farokhi. A review on the mechanics of nanostructures. International Journal of Engineering Science, 133, (2018), pp. 231–263.
H. M. Numanoğlu, B. Akgöz, and Ö. Civalek. On dynamic analysis of nanorods. International Journal of Engineering Science, 130, (2018), pp. 33–50.
A. Babaei and C. X. Yang. Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field. Microsystem Technologies, 25, (2019), pp. 1077–1085.
Ö. Civalek and H. M. Numanoğlu. Nonlocal finite element analysis for axial vibration of embedded love–bishop nanorods. International Journal of Mechanical Sciences, 188, (2020), pp. 105939–105956.
A. Babaei. Forced vibration analysis of non-local strain gradient rod subjected to harmonic excitations. Microsystem Technologies, 27, (2021), pp. 821–831.
H. Erol and M. Gürgöze. Longitudinal vibrations of a double-rod system coupled by springs and dampers. Journal of Sound and Vibration, 1, (2004), pp. 419–430.
T. Murmu and S. Adhikari. Nonlocal effects in the longitudinal vibration of double-nanorod systems. Physica E: Low-dimensional Systems and Nanostructures, 43, (2010), pp. 415–422.
S. Narendar and S. Gopalakrishnan. Axial wave propagation in coupled nanorod system with nonlocal small scale effects. Composites Part B: Engineering, 42, (2011), pp. 2013–2023.
D. Karliˇci´c, M. Caji´c, T. Murmu, and S. Adhikari. Nonlocal longitudinal vibration of viscoelastic coupled double-nanorod systems. European Journal of Mechanics-A/Solids, 49, (2015), pp. 183–196.
D. Xu, J. Du, and Y. Zhao. Longitudinal vibration analysis of elastically coupled nanorods system with general boundary supports. Sound & Vibration, 53, (2), (2019), pp. 16–28.
J. K. Zhou. Differential transformation and its applications for electrical circuits. Huazhong University Press, (1986).
Y. H. Chai and C. M.Wang. An application of differential transformation to stability analysis of heavy columns. International Journal of Structural Stability and Dynamics, 6, (2006), pp. 317–332.
V. Senthilkumar. Buckling analysis of a single-walled carbon nanotube with nonlocal continuum elasticity by using differential transform method. Advanced Science Letters, 3, (3), (2010), pp. 337–340.
V. Senthilkumar, S. C. Pradhan, and G. Prathap. Buckling analysis of a single-walled carbon nanotube with nonlocal continuum elasticity by using differential transform method. Advanced Science Letters, 3, (4), (2010), pp. 415–421.
V. Senthilkumar. Analyses of nonlocal nanostructures using differential transform method. PhD thesis, Indian Institute of Technology Kharagpur, West Bengal, India, (2015).
M. Aydogdu. 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, (2015), pp. 3132–3154.
K. Kiani and K. K. Żur. Vibrations of double-nanorod-systems with defects using nonlocalintegral-surface energy-based formulations. Composite Structures, 256, (2021), pp. 113028–113033.
M. Mohammadimehr, A. A. Monajemi, and M. Moradi. Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM. Journal of Mechanical Science and Technology, 29, (2015), pp. 2297–2305.
Z. Lv, H. Liu, and Q. Li. Effect of uncertainty in material properties on wave propagation characteristics of nanorod embedded in elastic medium. International Journal of Mechanics and Materials in Design, 14, (2018), pp. 375–392.
T. Murmu, S. Adhikari, and M. A. McCarthy. Axial vibration of embedded nanorods under transverse magnetic field effects via nonlocal elastic continuum theory. Journal of Computational and Theoretical Nanoscience, 11, (2014), pp. 1230–1236.
S. Gopalakrishnan and S. Narendar. Wave propagation in nanostructures: Nonlocal continuum mechanics formulations. Springer Science & Business Media, (2013).
C. Q. Ru. Column buckling of multiwalled carbon nanotubes with interlayer radial displacements. Physical Review B, 62, (24), (2000), pp. 16962–16967.
M. Aydogdu. Axial vibration analysis of nanorods (carbon nanotubes) embedded in an elastic medium using nonlocal elasticity. Mechanics Research Communications, 43, (2012), pp. 34–40.
P. Soltani and A. Farshidianfar. Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method. Applied Mathematical Modelling, 36, (8), (2012), pp. 3712–3724.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
