Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear forced vibration of FG-CNTs-reinforced curved microbeam based on strain gradient theory considering out-of-plane motion

  • Allahkarami, Farshid (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University) ;
  • Nikkhah-bahrami, Mansour (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University) ;
  • Saryazdi, Maryam Ghassabzadeh (Vehicle Technology Research Institute, Amirkabir University of Technology)
  • Received : 2017.09.14
  • Accepted : 2018.01.06
  • Published : 2018.03.25
⟨ Previous Next ⟩

Abstract

The main goal of this research is to examine the in-plane and out-of-plane forced vibration of a curved nanocomposite microbeam. The in-plane and out-of-plane displacements of the structure are considered based on the first order shear deformation theory (FSDT). The curved microbeam is reinforced by functionally graded carbon nanotubes (FG-CNTs) and thus the extended rule of mixture is employed to estimate the effective material properties of the structure. Also, the small scale effect is captured using the strain gradient theory. The structure is rested on a nonlinear orthotropic viscoelastic foundation and is subjected to concentrated transverse harmonic external force, thermal and magnetic loads. The derivation of the governing equations is performed using energy method and Hamilton's principle. Differential quadrature (DQ) method along with integral quadrature (IQ) and Newmark methods are employed to solve the problem. The effect of various parameters such as volume fraction and distribution type of CNTs, boundary conditions, elastic foundation, temperature changes, material length scale parameters, magnetic field, central angle and width to thickness ratio are studied on the frequency and force responses of the structure. The results indicate that the highest frequency and lowest vibration amplitude belongs to FGX distribution type while the inverse condition is observed for FGO distribution type. In addition, the hardening-type response of the structure with FGX distribution type is more intense with respect to the other distribution types.

Keywords

References

  1. Atci, D. and Bagdatli, S.M. (2017a), "Free vibrations of fluid conveying microbeams under non-ideal boundary conditions", Steel Compos. Struct., Int. J., 24(2), 141-149.
  2. Atci, D. and Bagdatli, S.M. (2017b), "Vibrations of fluid conveying microbeams under non-ideal boundary conditions", Microsyst. Technol., 23(10), 4741-4752. https://doi.org/10.1007/s00542-016-3255-y
  3. Allahkarami, F. and Nikkhah-bahrami, M. (2017), "Effects of agglomerated CNTs as reinforcement on the size-dependent vibration of embedded curved microbeams based on the modified couple stress theory", Mech. Adv. Mat. Struct., 1-14.
  4. Allahkarami, F., Nikkhah-bahrami, M. and Ghassabzadeh Saryazdi, M. (2017), "Magneto-thermo-mechanical dynamic buckling analysis of a FG-CNTs-reinforced curved microbeam with different boundary conditions using strain gradient theory", Int. J. Mech. Mater. Des., 1-19.
  5. Aydin Aya, S.A. and Tufekci, E. (2017), "Modeling and analysis of out-of-plane behavior of curved nanobeams based on nonlocal elasticity", Compos. Part B: Eng., 119, 184-195. https://doi.org/10.1016/j.compositesb.2017.03.050
  6. Bataineh, A.M. and Younis, M.I. (2015), "Dynamics of a clamped-clamped microbeam resonator considering fabrication imperfections", Microsyst. Technol., 21(11), 2425-2434. https://doi.org/10.1007/s00542-014-2349-7
  7. Dai, H.L., Wang, Y.K. and Wang, L. (2015), "Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory", Int. J. Eng. Sci., 94, 103-112. https://doi.org/10.1016/j.ijengsci.2015.05.007
  8. Dehrouyeh-Semnani, A.M., Dehrouyeh, M., Zafari-Koloukhi, H. and Ghamami, M. (2015), "Size-dependent frequency and stability characteristics of axially moving microbeams based on modified couple stress theory", Int. J. Eng. Sci., 97, 98-112. https://doi.org/10.1016/j.ijengsci.2015.09.003
  9. Dehrouyeh-Semnani, A.M., Mostafaei, H. and Nikkhah-Bahrami, M. (2016), "Free flexural vibration of geometrically imperfect functionally graded microbeams", Int. J. Eng. Sci., 105, 56-79. https://doi.org/10.1016/j.ijengsci.2016.05.002
  10. Erfani, S. and Akrami, V. (2016), "Evaluation of cyclic fracture in perforated beams using micromechanical fatigue model", Steel Compos. Struct., Int. J., 20(4), 913-930. https://doi.org/10.12989/scs.2016.20.4.913
  11. Ghayesh, M.H. and Farokhi, H. (2017), "Global dynamics of imperfect axially forced microbeams", Int. J. Eng. Sci., 115, 102-116.
  12. Ghayesh, M.H., Farokhi, H. and Gholipour, A. (2017), "Coupled vibrations of functionally graded Timoshenko microbeams", Europ. J. Mech. A/Solids, 65, 289-300. https://doi.org/10.1016/j.euromechsol.2017.04.009
  13. Gutschmidt, S. and Gottlieb, O. (2012), "Nonlinear dynamic behavior of a microbeam array subject to parametric actuation at low, medium and large DC-voltages", Nonlinear. Dyn., 67(1), 1-36. https://doi.org/10.1007/s11071-010-9888-y
  14. He, X.j., Wu, Q., Wang, Y., Song, M.x. and Yin, J.h. (2009), "Numerical simulation and analysis of electrically actuated microbeam-based MEMS capacitive switch", Microsyst. Technol., 15(2), 301-307. https://doi.org/10.1007/s00542-008-0702-4
  15. Jafari-Talookolaei, R.A., Abedi, M. and Attar, M. (2017), "Inplane and out-of-plane vibration modes of laminated composite beams with arbitrary lay-ups", Aerosp. Sci. Tech., 66, 366-379. https://doi.org/10.1016/j.ast.2017.02.027
  16. Jahangiri, R., Jahangiri, H. and Khezerloo, H. (2015), "FGM micro-gripper under electrostatic and intermolecular Van-der Waals forces using modified couple stress theory", Steel Compos. Struct., Int. J., 18(6), 1541-1555. https://doi.org/10.12989/scs.2015.18.6.1541
  17. Kolahchi, R. (2017b), "A comparative study on the bending vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC HDQ and DQ methods", Aerosp. Sci. Tech., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016
  18. Kolahchi, R. and Moniribidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech. -Engl Ed, 37(2), 265-274. https://doi.org/10.1007/s10483-016-2030-8
  19. Kolahchi, R., Rabani Bidgoli, M., Beygipoor, Gh. and Fakhar, M.H. (2015), "A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field", J. Mech. Sci. Tech., 29(9), 3669-3677. https://doi.org/10.1007/s12206-015-0811-9
  20. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos, Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032
  21. Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  22. Kolahchi, R., Zarei, M.Sh., Hajmohammad, M.H. and Naddaf Oskouei, A. (2017a), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169.
  23. Krylov, S., Ilic, B.R. and Lulinsky, S. (2011), "Bistability of curved microbeams actuated by fringing electrostatic fields", Nonlinear Dyn., 66(3), 403-411. https://doi.org/10.1007/s11071-011-0038-y
  24. Liu, B., Xing, Y., Wang, Z., Lu, X. and Sun, H. (2017), "Nonuniform rational Lagrange functions and its applications to isogeometric analysis of in-plane and flexural vibration of thin plates", Comput. Meth Appl. Mech. Eng., 321, 173-208. https://doi.org/10.1016/j.cma.2017.04.007
  25. Malekzadeh, P., Golbahar Haghighi, M.R. and Atashi, M.M. (2010), "Out-of-plane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct. 92(2), 541-552 . https://doi.org/10.1016/j.compstruct.2009.08.040
  26. Pan, F., Chen, Y., Liu, Y. and Guo, Z. (2017), "Out-of-plane bending of carbon nanotube films", Int. J. Solids Struct., 106-107, 183-199. https://doi.org/10.1016/j.ijsolstr.2016.11.020
  27. Peng, J., Yang, L., Lin, F. and Yang, J. (2017), "Dynamic analysis of size-dependent micro-beams with nonlinear elasticity under electrical actuation", Appl. Math. Model., 43, 441-453. https://doi.org/10.1016/j.apm.2016.11.025
  28. Rezaei, M.P. and Zamanian, M. (2017), "A two-dimensional vibration analysis of piezoelectrically actuated microbeam with nonideal boundary conditions", Physica E, 85, 285-293. https://doi.org/10.1016/j.physe.2016.09.005
  29. Rostami, H., Rahbar Ranji, A. and Bakhtiarinejad, F. (2016), "Free in-plane vibration analysis of rotating rectangular orthotropic cantilever plates", Int. J. Mech. Sci., 115-116, 438-456.
  30. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016), "Nonlinear vibration of axially functionally graded tapered microbeams", Int. J. Eng. Sci., 102, 12-26. https://doi.org/10.1016/j.ijengsci.2016.02.007
  31. Shen, H.Sh. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  32. Shen, H.Sh. and Zhang, Ch.L. (2011), "Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates", Comput. Mat. Sci., 50(3), 1022-1029. https://doi.org/10.1016/j.commatsci.2010.10.042
  33. Shu, C., Chew, Y.T. and Richards, E. (1995), "Generalized differential and integral quadrature and their application to solve boundary layer equations", Int. J. Num. Meth. Fluids, 21(9), 723-733. https://doi.org/10.1002/fld.1650210903
  34. Simsek, M. and Kocaturk, T. (2009), "Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load", J. Sound Vib., 320(1-2), 235-253. https://doi.org/10.1016/j.jsv.2008.07.012
  35. Wang, Ch., Ayalew, B., Rhyne, T., Cron, S. and Daolliez, B. (2016), "Forced in-plane vibration of a thick ring on a unilateral elastic foundation", J. Sound Vib., 380, 279-294.
  36. Wu, J.S. and Chiang, L.K. (2003), "Out-of-plane response of a circular Timoshenko beam due to moving load", Int. J. Solids Struct., 40(26), 7425-7448. https://doi.org/10.1016/j.ijsolstr.2003.07.004
  37. Younis, M.I. and Nayfeh, A.H. (2003), "A study of the nonlinear response of a resonant microbeam to an electric actuation", Nonlinear Dyn., 31(1), 91-117. https://doi.org/10.1023/A:1022103118330
  38. Zhang, B., He, Y., Liu, D., Gan, Zh. and Shen, L. (2013), "A novel size-dependent functionally graded curved mircobeam model based on the strain gradient elasticity theory", Compos. Struct., 106, 374-392. https://doi.org/10.1016/j.compstruct.2013.06.025

Cited by

  1. Exact third-order static and free vibration analyses of functionally graded porous curved beam vol.39, pp.1, 2021, https://doi.org/10.12989/scs.2021.39.1.001
  2. Higher order plate theory for buckling analysis of plates based on exact solution vol.40, pp.3, 2018, https://doi.org/10.12989/scs.2021.40.3.451