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Vibration analysis of nanotubes based on two-node size dependent axisymmetric shell element

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, size dependent axisymmetric shell element formulation is developed by using the modified couple stress theory in place of classical continuum theory. Since the study of nanoshells is conducted in nanodimensions, the mechanical properties of nanoshells are size dependent; therefore, taking into consideration the size effect, nonclassical continuum theories are used. In the present work the mass–stiffness matrix for axisymmetric shell element is developed, and by means of size-dependent finite element, the formulation is extended to more precisely account for nanotube vibration. It is shown that the classical axisymmetric shell element can also be defined by setting length scale parameter to zero in the equations. The results show that the rigidity of the nanoshell in the modified couple stress theory is greater than that in classical continuum theory, which leads to the increase in natural frequencies. The findings also indicate that the developed size dependent axisymmetric shell element is able to cover both cylindrical and conical shell elements and is reliable for simulating micro/nanoshells. Using size dependent axisymmetric shell element increases convergence speed and accuracy in addition to reducing the number of the required elements.
Rocznik
Strony
1345--1358
Opis fizyczny
Bibliogr. 21 poz., tab., wykr.
Twórcy
autor
  • Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran
autor
  • Faculty of Engineering, Shahrekourd University, Shahrekord, Iran
  • Nanotechnology Research Center, Shahrekord University, Shahrekord, Iran
Bibliografia
  • [1] M.M. Fotouhi, R.D. Firouz-Abadi, H. Haddadpour, Free vibration analysis of nanocones embedded in an elastic medium using a nonlocal continuum shell model, Int. J. Eng. Sci. 64 (2013) 14–22.
  • [2] M. Shojaeian, Y.T. Beni, Size-dependent electromechanical buckling of functionally graded electrostatic nano-bridges, Sens. Actuators A: Phys. 232 (2015) 49–62.
  • [3] R.D. Mindlin, H.F. Tiersten, Effects of couple-stresses in lineał elasticity, Arch. Rational Mech. Anal. 11 (1962) 415–448.
  • [4] F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct. 39 (2002) 2731–2743.
  • [5] N.A. Fleck, J.W. Hutchinson, Strain gradient plasticity, in: W. H. John, Y.W. Theodore (Eds.), Advances in Applied Mechanics, 1997, 295–361.
  • [6] D.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, J. Mech. Phys. Solids 51 (2003) 1477–1508.
  • [7] H.M. Ma, X.L. Gao, J.N. Reddy, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, J. Mech. Phys. Solids 56 (2008) 3379–3391.
  • [8] B. Akgöz, Ö. Civalek, Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory, Compos. Struct. 98 (2013) 314–322.
  • [9] J.N. Reddy, J. Berry, Nonlinear theories of axisymmetric bending of functionally graded circular plates with modified couple stress, Compos. Struct. 94 (2012) 3664–3668.
  • [10] Y. Tadi Beni, A. Koochi, M.R. Abadyan, Using modified couple stress theory for modeling the size dependent pull-in instability of torsional nano-mirror under Casimir force, Int. J. Optomechatronics 8 (2014) 47–71.
  • [11] M. Karimi Zeverdejani, Y. Tadi Beni, The nano scale vibration of protein microtubules based on modified strain gradient theory, Curr. Appl. Phys. 13 (2013) 1566–1576.
  • [12] B. Wang, J. Zhao, S. Zhou, A micro scale Timoshenko beam model based on strain gradient elasticity theory, Eur. J. Mech. A/Solids 29 (2010) 591–599.
  • [13] J. Zhao, S. Zhou, B. Wang, X. Wang, Nonlinear microbeam model based on strain gradient theory, Appl. Math. Model. 36 (2012) 2674–2686.
  • [14] H. Zeighampour, Y. Tadi Beni, Cylindrical thin-shell model based on modified strain gradient theory, Int. J. Eng. Sci. 78 (2014) 27–47.
  • [15] Z.C. Xia, J.W. Hutchinson, Crack tip fields in strain gradient plasticity, J. Mech. Phys. Solids 44 (1996) 1621–1648.
  • [16] S.-W. Chyuan, Computational simulation for MEMS comb drive levitation using FEM, J. Electrost. 66 (2008) 361–365.
  • [17] A. Zervos, P. Papanastasiou, I. Vardoulakis, Modelling of localization and scale in thick-walled cylinders with gradient elastoplasticity, Int. J. Solids Struct. 38 (2001) 5081–5095.
  • [18] P. Metz, G. Alici, G.M. Spinks, A finite element model for bending behavior of conducting polymer electromechanical actuators, Sens. Actuators A 130 (2006) 1–11.
  • [19] S.A. Tajalli, M. Moghimi Zand, M.T. Ahmadian, Effect of geometric nonlinearity on dynamic pull-in behavior of coupled-domain microstructures based on classical and shear deformation plate theories, Eur. J. Mech. A/Solids 28 (2009) 916–925.
  • [20] A.W. Leissa, Vibration of Shells, Published for the Acoustical Society of America through the American Institute of Physics, 1993.
  • [21] H. Zeighampour, Y. Tadi Beni, Analysis of conical shells in the framework of coupled stresses theory, Int. J. Eng. Sci. 81 (2014) 107–122.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fd7652e5-8fd3-405b-afde-9dd7ec6aac21
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