Dynamic response of FG-CNTRC beams subjected to a moving mass
Keywords:FG-CNTRC beams, third-order shear deformation theory, finite element method, moving mass
This article presents the forced vibration of composite beams reinforced by single-walled carbon nanotubes (SWCNTs) and subjected to a moving mass. Considering the distribution of carbon nanotubes such as uniform (UD-CNT), functionally graded Λ (FGΛ-CNT) and X (FGX-CNT), three different beams are studied. Based on a third-order shear deformation theory (TSDT), the motion equations of the beams are derived using Hamilton's principle. Including mass interaction forces, the motion equations are transformed into a finite element equation in which a two-node beam element with eight degrees of freedom is utilized. To improve the efficiency of the beam element, the transverse shear rotation is employed as an independent variable in the derivation of the beam element. The vibration characteristics, including the dynamic magnification factors and the time histories for mid-span deflections are computed by using the Newmark method. Numerical result reveal that the vibration of the beams is clearly influenced of the CNT reinforcement, and the dynamic magnification is significantly decreased by increasing the CNT volume fraction. It is also shown that the FGX-CNT beam is the best in dynamic resistance in terms of the lowest dynamic deflection and dynamic magnification factors. The effects of the total volume fraction and the moving load velocity on the dynamic behaviour of the functionally graded carbon nanotube reinforced composites (FG-CNTRC) beams are examined in detail and highlighted.
Bohlén M. and Bolton K. - Molecular dynamics studies of the influence of single wall carbon nanotubes on the mechanical properties of Poly(vinylidene fluoride), Comput. Mater. Sci. 68 (2013) 73-80. DOI: https://doi.org/10.1016/j.commatsci.2012.10.010
Han Y. and Elliott J. - Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites, Comput. Mater. Sci. 39 (2007) 315-323. DOI: https://doi.org/10.1016/j.commatsci.2006.06.011
Griebel M. and Hamaekers J. - Molecular dynamics simulations of the elastic moduli of polymer–carbon nanotube composites, Comput. Methods Appl. Mech. Engrg. 193 (2004) 1773-1788. DOI: https://doi.org/10.1016/j.cma.2003.12.025
Lu X. and Hu Z. - Mechanical property evaluation of single-walled carbon nanotubes by finite element modeling, Compos. Part B: Eng. 43 (2012) 1902-1913. DOI: https://doi.org/10.1016/j.compositesb.2012.02.002
Giannopoulos G. I., Kakavas P. A., and Anifantis N. K. - Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach, Comput.Mater. Sci. 41 (2008) 561-569. DOI: https://doi.org/10.1016/j.commatsci.2007.05.016
Shen H. S. - Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments, Compos. Struct. 91 (2009) 9-19. DOI: https://doi.org/10.1016/j.compstruct.2009.04.026
Ke L. L., Yang J., and Kitipornchai S. - Nonlinear free vibration of functionally graded carbon nanotubereinforced composite beams, Compos. Struct. 92 (2010) 676-683. DOI: https://doi.org/10.1016/j.compstruct.2009.09.024
Ke L. L., Yang J., and Kitipornchai S. - Dynamic stability of functionally graded carbon nanotube- reinforced composite beams, Mech. Adv. Mater. Struct. 20 (2013) 28-37. DOI: https://doi.org/10.1080/15376494.2011.581412
Yas M. H. and Heshmati M. - Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Appl. Math. Model. 36 (2012) 1371-94. DOI: https://doi.org/10.1016/j.apm.2011.08.037
Lin F. and Xiang Y. - Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories, Appl. Math. Model. 38 (2014) 3741-3754. DOI: https://doi.org/10.1016/j.apm.2014.02.008
Ansari R., Faghih Shojaei M., Mohammadi V., Gholami R., and Sadeghi F. - Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams, Compos. Struct. 13 (2014) 316-327. DOI: https://doi.org/10.1016/j.compstruct.2014.03.015
Aydogdu M. - On the vibration of aligned carbon nanotube reinforced composite beams, Adv. Nano Res. 2 (2014) 199-210. DOI: https://doi.org/10.12989/anr.2014.2.4.199
Wu. H. L., Yang J., and Kitipornchai S. - Nonlinear vibration of functionally graded carbon nanotube-reinforced composite beams with geometric imperfections, Compos. Part B: Eng. 90 (2016) 86-96. DOI: https://doi.org/10.1016/j.compositesb.2015.12.007
Chaudhari V. K. and Lal A. - Nonlinear Free Vibration Analysis of Elastically Supported Nanotube-reinforced Composite Beam in Thermal Environment, Proc. Eng. 144 (2016) 928-935. DOI: https://doi.org/10.1016/j.proeng.2016.05.119
Wu H., Kitipornchai S. and Yang J. - Imperfection sensitivity of thermal post-buckling behaviour of functionally graded carbon nanotube-reinforced composite beams, Appl. Math. Model. 42 (2017) 735-752. DOI: https://doi.org/10.1016/j.apm.2016.10.045
Gholami R., Ansari R., and Gholami Y. - Nonlinear resonant dynamics of geometrically imperfect higher-order shear deformable functionally graded carbon-nanotube reinforced composite beams, Compos. Struct. 174 (2017) 45-58. DOI: https://doi.org/10.1016/j.compstruct.2017.04.042
Shafiei H. and Setoodeh A. R. - Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation, Steel. Compos. Struct. 24 (2017) 65-77. DOI: https://doi.org/10.12989/scs.2017.24.1.065
Vo-Duy T., Ho-Huu V. and Nguyen-Thoi T. - Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method, Front. Struct. Civil. Eng. 13 (2019) 324-336. DOI: https://doi.org/10.1007/s11709-018-0466-6
Ranjbar M. and Feli S. - Temperature-dependent analysis of axially functionally graded CNT reinforced micro-cantilever beams subjected to low velocity impact, Mech. Adv. Mater. Struct. 26 (2019) 1154-1168. DOI: https://doi.org/10.1080/15376494.2018.1432788
Fallah A., Dehkordi M. B., Nourbakhsh H., and Beni Y. T. - Semi-exact solution for nonlinear dynamic analysis of graded carbon nanotube-reinforced beam with graded shape memory wires, Mech. Adv. Mater. Struct. 28 (2019) 1-15. DOI: https://doi.org/10.1080/15376494.2019.1578012
Palacios J. A. and Ganesan R. - Dynamic response of Carbon-Nanotube-Reinforced-Polymer materials based on multiscale finite element analysis, Compos. Part B: Eng. 166 (2019) 497-508. DOI: https://doi.org/10.1016/j.compositesb.2019.02.039
Shi G. - A new simple third-order shear deformation theory of plates, Int. J. Solids Struct. 44 (2007) 4399-417. DOI: https://doi.org/10.1016/j.ijsolstr.2006.11.031
Shi G., Lam K. Y. and Tay T. E. - On efficient finite element modeling of composite beams and plates using higher-order theories and an accurate composite beam element, Compos. Struct. 41 (1998) 159-165. DOI: https://doi.org/10.1016/S0263-8223(98)00050-6
Esen I. -Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass, Int. J. Mech. Sci. 153–154 (2019) 21-35. DOI: https://doi.org/10.1016/j.ijmecsci.2019.01.033
Esen I. - A new finite element for transverse vibration of rectangular thin plates under a moving mass, Finite Elem. Anal. Des. 66 (2013) 26-35. DOI: https://doi.org/10.1016/j.finel.2012.11.005
How to Cite
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Vietnam Journal of Sciences and Technology (VJST) is an open access and peer-reviewed journal. All academic publications could be made free to read and downloaded for everyone. In addition, articles are published under term of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA) Licence which permits use, distribution and reproduction in any medium, provided the original work is properly cited & ShareAlike terms followed.
Copyright on any research article published in VJST is retained by the respective author(s), without restrictions. Authors grant VAST Journals System a license to publish the article and identify itself as the original publisher. Upon author(s) by giving permission to VJST either via VJST journal portal or other channel to publish their research work in VJST agrees to all the terms and conditions of https://creativecommons.org/licenses/by-sa/4.0/ License and terms & condition set by VJST.
Authors have the responsibility of to secure all necessary copyright permissions for the use of 3rd-party materials in their manuscript.