Stability analysis of single-walled carbon nanotubes embedded in winkler foundation placed in a thermal environment considering the surface effect using a new refined beam theory

References

• Akgöz, B., and Ö. Civalek. 2011. Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories. Journal of Computational and Theoretical Nanoscience 8 (9):1821–7. doi:10.1166/jctn.2011.1888.
   Google Scholar
• Arefi, M., and A. H. Soltan Arani. 2018. Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments. Mechanics Based Design of Structures and Machines 46 (6):669–92. doi:10.1080/15397734.2018.1434002.
   Web of Science ®Google Scholar
• Berghouti, H., E. A. Adda Bedia, A. Benkhedda, and A. Tounsi. 2019. Vibration analysis of nonlocal porous nanobeams made of functionally graded material. Advances in Nano Research 7 (5):351–64.
   Web of Science ®Google Scholar
• Bedia, W. A., M. S. Houari, A. Bessaim, A. A. Bousahla, A. Tounsi, T. Saeed, and M. S. Alhodaly. 2019. A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams. Journal of Nano Research 57:175–91. doi:10.4028/www.scientific.net/JNanoR.57.175.
   Web of Science ®Google Scholar
• Chaabane, L. A., F. Bourada, M. Sekkal, S. Zerouati, F. Z. Zaoui, A. Tounsi, A. Derras, A. A. Bousahla, and A. Tounsi. 2019. Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation. Structural Engineering and Mechanics 71 (2):185–96.
   Web of Science ®Google Scholar
• Chang, W. J., and H. L. Lee. 2013. Free vibration of an embedded conical nanotube with surface effect. Digest Journal of Nanomaterials and Biostructures 8:1325–33.
   Web of Science ®Google Scholar
• Chen, X., C. Q. Fang, and X. Wang. 2017. The influence of surface effect on vibration behaviors of carbon nanotubes under initial stress. Physica E: Low-Dimensional Systems and Nanostructures 85:47–55. doi:10.1016/j.physe.2016.08.011.
   Web of Science ®Google Scholar
• Dastjerdi, S., and Y. T. Beni. 2019. A novel approach for nonlinear bending response of macro-and nanoplates with irregular variable thickness under nonuniform loading in thermal environment. Mechanics Based Design of Structures and Machines 47 (4):1–26. doi:10.1080/15397734.2018.1557529.
   Web of Science ®Google Scholar
• Draiche, K., A. A. Bousahla, A. Tounsi, A. S. Alwabli, A. Tounsi, and S. R. Mahmoud. 2019. Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory. Computers and Concrete 24 (4):369–78.
   Web of Science ®Google Scholar
• Draoui, A., M. Zidour, A. Tounsi, and B. Adim. 2019. Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT). Journal of Nano Research 57:117–35. doi:10.4028/www.scientific.net/JNanoR.57.117.
   Web of Science ®Google Scholar
• Eringen, A. C. 1972. Nonlocal polar elastic continua. International Journal of Engineering Science 10 (1):1–16. doi:10.1016/0020-7225(72)90070-5.
   Web of Science ®Google Scholar
• Farshi, B., A. Assadi, and A. Alinia-Ziazi. 2010. Frequency analysis of nanotubes with consideration of surface effects. Applied Physics Letters 96 (9):093105. doi:10.1063/1.3332579.
   Web of Science ®Google Scholar
• Fattahi, A. M., S. Sahmani, and N. A. Ahmed. 2019. Nonlocal strain gradient beam model for nonlinear secondary resonance analysis of functionally graded porous micro/nano-beams under periodic hard excitations. Mechanics Based Design of Structures and Machines 1–30. doi:10.1080/15397734.2019.1624176.
   Web of Science ®Google Scholar
• Jena, S. K., and S. Chakraverty. 2018a. Free vibration analysis of variable cross-section single layered graphene nano-ribbons (SLGNRs) using differential quadrature method. Frontiers in Built Environment 4:63. doi:10.3389/fbuil.2018.00063.
   Google Scholar
• Jena, S. K., and S. Chakraverty. 2018b. Free vibration analysis of single walled carbon nanotube with exponentially varying stiffness. Curved and Layered Structures 5 (1):201–12. doi:10.1515/cls-2018-0015.
   Web of Science ®Google Scholar
• Jena, S. K., and S. Chakraverty. 2018c. Free vibration analysis of Euler-Bernoulli Nano beam using differential transform method. International Journal of Computational Materials Science and Engineering 07 (03):1850020. doi:10.1142/S2047684118500203.
   Web of Science ®Google Scholar
• Jena, S. K., and S. Chakraverty. 2019a. Differential quadrature and differential transformation methods in Buckling analysis of nanobeams. Curved and Layered Structures 6 (1):68–76. doi:10.1515/cls-2019-0006.
   Web of Science ®Google Scholar
• Jena, S. K., and S. Chakraverty. 2019b. Dynamic behavior of electro-magnetic nanobeam using haar wavelet method (HWM) and higher Order haar wavelet method (HOHWM). The European Physical Journal Plus 134 (10):538. doi:10.1140/epjp/i2019-12874-8.
   Web of Science ®Google Scholar
• Jena, S. K., and S. Chakraverty. 2019c. Dynamic analysis of single-layered graphene nano-ribbons (SLGNRs) with variable cross-section resting on elastic foundation. Curved and Layered Structures 6 (1):132–45. doi:10.1515/cls-2019-0011.
   Web of Science ®Google Scholar
• Jena, S. K., S. Chakraverty, and R. M. Jena. 2019. Propagation of uncertainty in free vibration of Euler-Bernoulli nanobeam. Journal of the Brazilian Society of Mechanical Sciences and Engineering 41 (10):436. doi:10.1007/s40430-019-1947-9.
   Web of Science ®Google Scholar
• Jena, S. K., S. Chakraverty, R. M. Jena, and F. Tornabene. 2019. A novel fractional nonlocal model and its application in buckling analysis of Euler-Bernoulli nanobeam. Materials Research Express 6 (5):055016. doi:10.1088/2053-1591/ab016b.
   Web of Science ®Google Scholar
• Jena, S. K., S. Chakraverty, and M. Malikan. 2019. Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium. Engineering with Computers. doi:10.1007/s00366-019-00883-1.
   Web of Science ®Google Scholar
• Jena, S. K., S. Chakraverty, and F. Tornabene. 2019a. Vibration characteristics of nanobeam with exponentially varying flexural rigidity resting on linearly varying elastic foundation using differential quadrature method. Materials Research Express 6 (8):085051. doi:10.1088/2053-1591/ab1f47.
   Web of Science ®Google Scholar
• Jena, S. K., S. Chakraverty, and F. Tornabene. 2019b. Dynamical behavior of nanobeam embedded in constant, linear, parabolic, and sinusoidal types of Winkler elastic foundation using first-order nonlocal strain gradient model. Materials Research Express 6 (8):0850f2. doi:10.1088/2053-1591/ab2779.
   Web of Science ®Google Scholar
• Jena, S. K., S. Chakraverty, and F. Tornabene. 2019c. Buckling behavior of nanobeam placed in an electro-magnetic field using shifted Chebyshev polynomials based Rayleigh-Ritz method. Nanomaterials 9 (9):1326. doi:10.3390/nano9091326.
   Web of Science ®Google Scholar
• Larbi, L.O., A. Kaci, M. S. A. Houari, and A. Tounsi. 2013. An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams. Mechanics Based Design of Structures and Machines 41 (4):421–33. doi:10.1080/15397734.2013.763713.
   Web of Science ®Google Scholar
• Lee, H. L., and W. J. Chang. 2010. Surface effects on frequency analysis of nanotubes using nonlocal Timoshenko beam theory. Journal of Applied Physics 108 (9):093503. doi:10.1063/1.3503853.
   Web of Science ®Google Scholar
• Li, L., and Y. Hu. 2015. Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. International Journal of Engineering Science 97:84–94. doi:10.1016/j.ijengsci.2015.08.013.
   Web of Science ®Google Scholar
• Malikan, M. 2017. Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory. Applied Mathematical Modelling 48:196–207. doi:10.1016/j.apm.2017.03.065.
   Web of Science ®Google Scholar
• Malikan, M. 2019. On the buckling response of axially pressurized nanotubes based on a novel nonlocal beam theory. Journal of Applied and Computational Mechanics 5:103–12.
   Web of Science ®Google Scholar
• Malikan, M., and S. Dastjerdi. 2018. Analytical buckling of FG nanobeams on the basis of a new one variable first-order shear deformation beam theory. International Journal of Engineering & Applied Sciences 10:21–34. doi:10.24107/ijeas.420838.
   Google Scholar
• Malikan, M., R. Dimitri, and F. Tornabene. 2019. Transient response of oscillated carbon nanotubes with an internal and external damping. Composites Part B: Engineering 158:198–205. doi:10.1016/j.compositesb.2018.09.092.
   Web of Science ®Google Scholar
• Malikan, M., and V. B. Nguyen. 2018. Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory. Physica E: Low-Dimensional Systems and Nanostructures 102:8–28. doi:10.1016/j.physe.2018.04.018.
   Web of Science ®Google Scholar
• Malikan, M., V. B. Nguyen, R. Dimitri, and F. Tornabene. 2019. Dynamic modeling of non-cylindrical curved viscoelastic single-walled carbon nanotubes based on the second gradient theory. Materials Research Express 6 (7):075041. doi:10.1088/2053-1591/ab15ff.
   Web of Science ®Google Scholar
• Malikan, M., V. B. Nguyen, and F. Tornabene. 2018a. Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory. Engineering Science and Technology. An International Journal 21:778–86. doi:10.1016/j.jestch.2018.06.001.
   Web of Science ®Google Scholar
• Malikan, M., V. B. Nguyen, and F. Tornabene. 2018b. Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory. Materials Research Express 5 (7):075031. doi:10.1088/2053-1591/aad144.
   Web of Science ®Google Scholar
• Malikan, M., F. Tornabene, and R. Dimitri. 2018. Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals. Materials Research Express 5 (9):095006. doi:10.1088/2053-1591/aad4c3.
   Web of Science ®Google Scholar
• Medani, M., A. Benahmed, M. Zidour, H. Heireche, A. Tounsi, A. A. Bousahla, A. Tounsi, and S. R. Mahmoud. 2019. Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle. Steel and Composite Structures 32 (5):595–610.
   Web of Science ®Google Scholar
• Mehralian, F., Y. T. Beni, and M. Karimi Zeverdejani. 2017. Calibration of nonlocal strain gradient shell model for buckling analysis of nanotubes using molecular dynamics simulations. Physica B: Condensed Matter 521:102–11. doi:10.1016/j.physb.2017.06.058.
   Web of Science ®Google Scholar
• Murmu, T., and S. C. Pradhan. 2010. Thermal effects on the stability of embedded carbon nanotubes. Computational Materials Science 47 (3):721–7. doi:10.1016/j.commatsci.2009.10.015.
   Web of Science ®Google Scholar
• Pradhan, S. C., and G. K. Reddy. 2011. Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM. Computational Materials Science 50 (3):1052–6. doi:10.1016/j.commatsci.2010.11.001.
   Web of Science ®Google Scholar
• Semmah, A., H. Heireche, A. A. Bousahla, and A. Tounsi. 2019. Thermal buckling analysis of SWBNNT on Winkler foundation by non-local FSDT. Advances in Nano Research 7 (2):89. doi:10.12989/anr.2017.5.1.001.
   Web of Science ®Google Scholar
• She, G. L., F. G. Yuan, Y. R. Ren, and W. Sh Xiao. 2017. On buckling and post buckling behavior of nanotubes. International Journal of Engineering Science 121:130–42. doi:10.1016/j.ijengsci.2017.09.005.
   Web of Science ®Google Scholar
• Sun, D.-L., and X.-F. Li. 2019. Initial value method for free vibration of axially loaded functionally graded Timoshenko beams with nonuniform cross section. Mechanics Based Design of Structures and Machines 47 (1):102–20. doi:10.1080/15397734.2018.1526690.
   Web of Science ®Google Scholar
• Teifouet, M., A. Robinson, and S. Adali. 2017. Buckling of nonuniform carbon nanotubes under concentrated and distributed axial loads. Mechanical Sciences 8:299–305. doi:10.5194/ms-8-299-2017.
   Web of Science ®Google Scholar
• Thai, H.-T. 2012. A nonlocal beam theory for bending, buckling, and vibration of nanobeams. International Journal of Engineering Science 52:56–64. doi:10.1016/j.ijengsci.2011.11.011.
   Web of Science ®Google Scholar
• Wang, B. L., M. Hoffman, and A. B. Yu. 2012. Buckling analysis of embedded nanotubes using gradient continuum theory. Mechanics of Materials 45:52–60. doi:10.1016/j.mechmat.2011.10.003.
   Web of Science ®Google Scholar
• Wang, C. M., Y. Y. Zhang, S. S. Ramesh, and S. Kitipornchai. 2006. Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory. Journal of Physics D: Applied Physics 39 (17):3904–9. doi:10.1088/0022-3727/39/17/029.
   Web of Science ®Google Scholar
• Zhen, Y. X. 2017. Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects. Physica E: Low-Dimensional Systems and Nanostructures 86:275–9. doi:10.1016/j.physe.2016.10.037.
   Web of Science ®Google Scholar