[1] I. Kang et al., "Introduction to carbon nanotube and nanofiber smart materials," Composites Part B: Engineering, vol. 37, no. 6, pp. 382-394, 2006.
[2] S. Iijima, "Helical microtubules of graphitic carbon," nature, vol. 354, no. 6348, pp. 56-58, 1991.
[3] C. Gutsche, "S. Reich, C. Thomsen, J. Maultzsch: Carbon nanotubes, basic concepts and physical properties: Wiley-VCH, 2004," ed: Springer, 2004.
doi:10.1007/s00396-004-1180-6
[4] J. Yoon, C. Ru, and A. Mioduchowski, "Vibration of an embedded multiwall carbon nanotube," Composites Science and Technology, vol. 63, no. 11, pp. 1533-1542, 2003.
[5] C. Wang, V. Tan, and Y. Zhang, "Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes," Journal of Sound and Vibration, vol. 294, no. 4-5, pp. 1060-1072, 2006.
[6] T. Murmu and S. Pradhan, "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory," Computational Materials Science, vol. 46, no. 4, pp. 854-859, 2009.
[7] M. Şimşek, "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, vol. 43, no. 1, pp. 182-191, 2010. doi:10.1016/j.physe.2010.07.003
[8] R. Ansari and H. Rouhi, "Analytical treatment of the free vibration of single-walled carbon nanotubes based on the nonlocal Flugge shell theory," J. Eng. Mater. Technol. 2012, vol. 134, no. 1, pp. 011008, 2012. doi:10.1115/1.4005347
[9] R. Ansari, H. Rouhi, and B. Arash, "Vibrational analysis of double-walled carbon nanotubes based on the nonlocal Donnell shell theory via a new numerical approach," IJST, Transactions of Mechanical Engineering, Vol. 37, No. M2, pp 91-105, 2013. doi:10.22099/ijstm.2013.1740
[10] S. Pradhan and U. Mandal, "Finite element analysis of CNTs based on nonlocal elasticity and Timoshenko beam theory including thermal effect," Physica E: Low-dimensional Systems and Nanostructures, vol. 53, pp. 223-232, 2013.
[11] R. Ansari Khalkhali, A. Norouzzadeh, R. Gholami, "Forced vibration analysis of conveying fluid carbon nanotube resting on elastic foundation based on modified couple stress theory, " Modares Mechanical Engineering, Vol. 15, No. 3, pp. 27-34, 2015 (In Persian), doi:20.1001.1.10275940.1394.15.3.34.4
[12] H, Ramezannejad Azarboni, H. Keshavarzpour Primary resonance analysis of a curved single walled carbon nanotubes on the viscoelastic medium in thermal environment under harmonic force. Modares Mechanical Engineering 18 (5), pp.211-217, 2018; (In Persian), dor:20.1001.1.10275940.1394.15.3.34.4
[13] B. Shahriari, , M.T. Ahmadian, V. Ghorbanian Kerdabadi, "Investigation of curved shaped carbon nano tubes behavior on an elastic foundation due to sinusoidal load using nonlocal elasticity theory." Modares Mechanical Engineering, pp. 199-209. 2017, (In Persian), dor:20.1001.1.10275940.1395.16.11.35.8
[14] J. A. Palacios and R. Ganesan, "Dynamic response of single-walled carbon nanotubes based on various shell theories," Journal of Reinforced Plastics and Composites, vol. 38, no. 9, pp. 413-425, 2019.
[15] M. Kamali Moghaddam, M. Tahani, "Study the effect of environment temperature on mechanical and fracture behavior of carbon nanotubes, " Modares Mechanical Engineering, Vol. 17, No. 3, pp. 87-92, 2017 (in Persian)
doi:20.1001.1.10275940.1396.17.3.42.6
[16] S. Asghar, M. N. Naeem, and M. Hussain, "Non-local effect on the vibration analysis of double walled carbon nanotubes based on Donnell shell theory," Physica E: Low-dimensional Systems and Nanostructures, vol. 116, p. 113726, 2020.
[17] M. A. De Rosa, M. Lippiello, A. Onorato, and I. Elishakoff, "Free vibration of single-walled carbon nanotubes using nonlocal truncated Timoshenko-Ehrenfest beam theory," Applied Mechanics, vol. 4, no. 2, pp. 699-714, 2023.
[18] J. Chen et al., "Transverse vibration analysis of double-walled carbon nanotubes in an elastic medium under temperature gradients and electrical fields based on nonlocal Reddy beam theory," Materials Science and Engineering: B, vol. 291, p. 116220, 2023.
[19] I. Ahmadi, M. Davarpanah, J. Sladek, V. Sladek, and M. N. Moradi, "A size-dependent meshless model for free vibration analysis of 2D-functionally graded multiple nanobeam system," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 46, no. 1, p. 11, 2024. doi:10.1007/s40430-023-04580-5
[20] I. Ahmadi, M. N. Moradi, and M. D. Panah, "Dynamic response analysis of nanoparticle-nanobeam impact using nonlocal theory and meshless method," Struct. Eng. Mech, vol. 89, no. 2, p. 135, 2024.
doi:10.12989/sem.2024.89.2.000
[21] M. Strozzi, I. E. Elishakoff, M. Bochicchio, M. Cocconcelli, R. Rubini, and E. Radi, "Nonlocal Strain Gradient Anisotropic Elastic Shell Model for Vibration Analysis of Single‒walled Carbon Nanotubes," 2024.
doi: 10.20944/preprints202401.0806.v1
[22] S. K. Jena, S. Pradyumna, and S. Chakraverty, "Thermal vibration of armchair, chiral, and zigzag types of single walled carbon nanotubes using a nonlocal elasticity theory: An analytical approach," ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, vol. 104, no. 4, p. e202301047, 2024.
doi:10.1002/zamm.202301047
[23] A. Tepe, "Vibration analysis of SWCNTs resting on an elastic foundation using the initial values method: A. Tepe," Journal of Engineering Mathematics, vol. 152, no. 1, p. 20, 2025.
doi:10.1007/s10665-025-10465-4
[24] E. K. Echouai, A. Adri, O. Outassafte, Y. El Khouddar, I. El Hantati, and R. Benamar, "Analysis of the Transverse Vibrations of a Carbon Nanotube Resting on a Winkler Foundation Subjected to Low-Temperature Thermal Load," in Advanced Materials for Sustainable Energy and Engineering: Volume 1: Novel Nanomaterials for Sustainable Energy: Springer, 2025, pp. 41-53.
doi:10.1007/978-3-031-75032-8_4
[25] E. K. Echouai et al., "The Effect of Temperature Change on the Transverse Vibration Frequencies of a Carbon Nanotube," in the Proceedings of the International Conference on Smart City Applications, 2024: Springer, pp. 536-547.
[26] X. Zhang, "Parametric analysis of frequency of rotating laminated composite cylindrical shells with the wave propagation approach," Computer methods in applied mechanics and engineering, vol. 191, no. 19-20, pp. 2057-2071, 2002.
[27] A. C. Eringen, "Theories of nonlocal plasticity," International Journal of Engineering Science, vol. 21, no. 7, pp. 741-751, 1983.
[28] C. Shu, Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. University of Glasgow (United Kingdom), 1991. https://theses.gla.ac.uk/id/eprint/77274
[29] A. Alibeigloo and M. Shaban, "Free vibration analysis of carbon nanotubes by using three-dimensional theory of elasticity," Acta Mechanica, vol. 224, pp. 1415-1427, 2013.
doi:10.1007/s00707-013-0817-2
[30] M. A. Khadimallah, M. Hussain, M. Taj, H. Ayed, and A. Tounsi, "Parametric vibration analysis of single-walled carbon nanotubes based on Sanders shell theory," Advances in Nano Research, vol. 10, no. 2, pp. 165-174, 2021. doi:10.12989/anr.2021.10.2.165
