Structural Engineering and Mechanics

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Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM

  • Mohammadimehr, M. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Alimirzaei, S. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2015.05.21
  • Accepted : 2016.04.11
  • Published : 2016.08.10
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Abstract

In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.

Keywords

Acknowledgement

Supported by : University of Kashan

References

  1. Akbas, S.D. (2015), "Large deflection analysis of edge cracked simple supported beams", Struct. Eng. Mech., 54(3), 433-451 https://doi.org/10.12989/sem.2015.54.3.433
  2. Ansari, R. and Ramezannezhad, S. (2011), "Nonlocal Timoshenko beam model for the large-amplitude vibrations of embedded multiwalled carbon nanotubes including thermal effects", Physica. E., 43, 1171-1178. https://doi.org/10.1016/j.physe.2011.01.024
  3. Bouiadjra, B.B., Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  4. Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028
  5. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Model., 37, 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  6. Farshidianfar, A. and Soltani, P. (2012), "Nonlinear flow-induced vibration of a SWCNT with a geometrical imperfection", Comput. Mater. Sci., 53, 105-116. https://doi.org/10.1016/j.commatsci.2011.08.014
  7. Ghorbanpour Arani, A., Atabakhshian, V., Loghman, A., Shajari, A.R. and Amir, S. (2012), "Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method", Physica B., 407, 2549-2555. https://doi.org/10.1016/j.physb.2012.03.065
  8. Heshmati, M. and Yas, M.H. (2013), "Vibrations of non-uniform functionally graded MWCNTs-polystyrene nano-composite beams under action of moving load", Mater. Des., 46, 206-218. https://doi.org/10.1016/j.matdes.2012.10.002
  9. Lau, K.T., Gu, C., Gao, G.H., Ling, H.Y. and Reid, S. (2004), "Stretching process of single and multiwalled carbon nanotubes for nanocomposite", Appl. Carbon., 42, 8-426.
  10. Li, C. (2013), "Size-dependent thermal behaviors of axially traveling nanobeams based on a strain gradient theory", Struct. Eng. Mech., 48(3), 415-434. https://doi.org/10.12989/sem.2013.48.3.415
  11. Li, Z.M. (2014), "Thermal post buckling behavior of 3D braided beams with initial geometric imperfection under different type temperature distributions", Compos. Struct., 108, 924-936. https://doi.org/10.1016/j.compstruct.2013.10.028
  12. Liew, K.M., Lei, Z.X. and Zhan, L.W. (2015), "Mechanical analysis of functionally graded carbon nanotube reinforced composites", A Review, Compos. Struct., 120,90-97. https://doi.org/10.1016/j.compstruct.2014.09.041
  13. Mohammadimehr, M. and Mostafavifar, M. (2016), "Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT", Compos. Part B: Eng., 94(1), 253-270. https://doi.org/10.1016/j.compositesb.2016.03.030
  14. Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of single-walled boron nitride nanorods under electric excitation", Turk J. Eng. Environ. Sci., 37, 1-15.
  15. Mohammadimehr, M., Mohandes, M. and Moradi, M. (2016a), "Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory", J.Vib. Control, 22(7), 1790-1807. https://doi.org/10.1177/1077546314544513
  16. Mohammadimehr, M., Monajemi, A.A. and Moradi, M. (2015a), "Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM", J. Mech. Sci. Technol., 29(6), 2297-2305. https://doi.org/10.1007/s12206-015-0522-2
  17. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015b), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077
  18. Mohammadimehr, M., Salemi, M. and Rousta Navi, B. (2016b), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermo-mechanical loadings using DQM", Compos. Struct., 138, 361-380. https://doi.org/10.1016/j.compstruct.2015.11.055
  19. Narendar, S., Gupta, S.S. and Gopalakrishnan, S. (2012), "Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 36, 4529-4538. https://doi.org/10.1016/j.apm.2011.11.073
  20. Putcha, N.S. and Refined, A. (1986), "Mixed shear flexible finite element for the nonlinear analysis of laminated plates",Comput. Struct., 22, 529-538. https://doi.org/10.1016/0045-7949(86)90002-7
  21. Rahmati, A.H. and Mohammadimehr, M. (2014), "Vibration analysis of non-uniform and non-homogeneous boron nitride nanorods embedded in an elastic medium under combined loadings using DQM", Physica B., 440, 88-98. https://doi.org/10.1016/j.physb.2014.01.036
  22. Ranjan, R. (2011), "Nonlinear finite element analysis of bending of straight beams using hp-spectral approximations", J. Solid. Mech., 3, 96-113.
  23. Reddy, J.N. (1987),"Mixed finite element models for laminated composite plate", J. Eng. Indus., 109, 39-45. https://doi.org/10.1115/1.3187092
  24. Reddy, J.N. (2004), An Introduction to nonlinear finite element analysis, Oxford University Press, Oxford, New York, USA.
  25. Simsek, M. (2014), "Nonlinear static and free vibration analysis of microbeams based on the nonlinear elastic foundation using modified couple stress theory and He's variational method", Compos. Struct., 12, 264-272.
  26. Wang, B., Deng, Z., Ouyang, H. and Zhou, J. (2015), "Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory", Physica. E., 66, 283-292. https://doi.org/10.1016/j.physe.2014.09.015
  27. Wang, B., Deng, Z.C. and Zhang, K. (2013), "Nonlinear vibration of embedded single walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory", Appl. Math. Mech., Engl. Ed. (English Edition), 34(3), 269-280. https://doi.org/10.1007/s10483-013-1669-8
  28. Yas, M.H. and Heshmati, M. (2012), "Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load", Appl. Math. Model., 36, 1371-1394. https://doi.org/10.1016/j.apm.2011.08.037
  29. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Press. Ves. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012

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