[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Nonlinear Random Vibration of Micro-Beams Resting on Visco-Elastic Foundation via the Modified Couple Stress Theory

Journal of Applied Nonlinear Dynamics 12(4) (2023) 707--721 | DOI:10.5890/JAND.2023.12.006

Dang Van Hieu, Nguyen Thi Hoa

Department of Mechanics, Faculty of Automotive and Power Machinery Engineering, Thai Nguyen University of

Technology, Thainguyen, Vietnam

Download Full Text PDF

 

Abstract

The aim of this paper is to present an analytical analysis of nonlinear random vibration behaviors of micro-beams resting on a visco-elastic foundation. The modif\`{i}ed couple stress theory and the Euler-Bernoulli beam theory (EBT) with the von-K\'{a}rm\'{a}n's geometrical nonlinearity are employed for this analysis. The equation of motion of the micro-beam is established based on the Hamilton's principle. The input excitation is assumed to be a Gaussian process with zero mean. The mean-square of the micro-beam's displacement is found by the regaluted equivalent linearization method. Comparison of the obtained solutions with the published solutions and the classical solutions shows the accuracy. The influences of the material length scale parameter (MLSP), the spectral density of the input excitation and the coefficients of the visco-elastic foundation on the nonlinear random vibration response of micro-beams are investigated in detail.

References

  1. [1]  Zhang, W.M., Yan, H., Peng, Z.K., and Meng, G. (2014), Electrostatic pull-in instability in MEMS/NEMS: A review, Sensors and Actuators A, 214, 187-218.
  2. [2]  Fleck, N.A., Muller, G.M., Ashby, M.F., and Hutchinson, J.W. (1994), Strain gradient plasticity: theory and experiment, Acta Metallurgicaet Materialia, 42(2), 475-487.
  3. [3]  St\"{o}lken, J.S. and Evans, A.G. (1998), A microbend test method for measuring the plasticity length scale, Acta Materialia, 46(14), 5109-5115.
  4. [4]  Eringen, A.C. and Edelen, D.G.B. (1972), On nonlocal elasticity, International Journal of Engineering Science, 10, 233-248.
  5. [5]  Eringen, A.C. (1983), On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 4703-4710.
  6. [6]  Mindlin, R.D. and Tiersten, H.F. (1962), Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11(1), 415-44.
  7. [7]  Mindlin, R.D. (1965), Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, 1(1), 417-438.
  8. [8]  Yang, F., Chong, A.C.M., Lam, D.C.C., and Tong, P. (2002), Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10), 2731-2743.
  9. [9]  Thai, H.T. (2012), A nonlocal beam theory for bending, buckling, and vibration of nanobeams, International Journal of Engineering Science, 52, 56-64.
  10. [10]  Sayyad, A.S. and Ghugal, Y.M. (2020), Bending, buckling and free vibration analysis of size-dependent nanoscale FG beams using refined models and Eringen's nonlocal theory, International Journal of Applied Mechanics, 12(A2001), 2050007.
  11. [11]  Wang, B., Zhao, J., and Zhou, S. (2010), A micro scale Timoshenko beam model based on strain gradient elasticity theory, European Journal of Mechanics A/Solids, 29, 591-599.
  12. [12]  Akg\"{o}z, B. and Civalek, \"{O}. (2013), A size-dependent shear deformation beam model based on the strain gradient elasticity theory, International Journal of Engineering Science, 70, 1-14.
  13. [13]  Sedighi, H.M. (2014), Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory, Acta Astronautica, 95, 111-123.
  14. [14]  \c{S}im\c{s}ek, 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, Composite Structures, 112, 264-272.
  15. [15]  Mollamahmuto\u{g}lu, \c{C}. and Mercan, A. (2019), A novel functional and mixed finite element analysis of functionally graded microbeams based on modified couple stress theory, Composite Structures, 223, 110950.
  16. [16]  Beni, Z.T., Ravandi, S.A.H., and Beni, Y.T. (2021), Size-dependent nonlinear forced vibration analysis of viscoelastic/piezoelectric nano-beam, Journal of Applied and Computational Mechanics, 7(4), 1878-1891.
  17. [17]  Akg\"{o}z, B. and Civalek, \"{O}. (2017), A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by Pasternak elastic foundation, Composite Structures, 176, 1028-1038.
  18. [18]  Akg\"{o}z, B. and Civalek, \"{O}. (2012), Investigation of size effects on static response of single-walled carbon nanotubes based on strain gradient elasticity, International Journal of Computational Methods, 9(02), 1240032.
  19. [19]  Mercan, K., Numanoglu, H.M., Akg\"{o}z, B., Demir, C., and Civalek, \"{O}. (2017), Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix, Archive of Applied Mechanics, 87(11), 1797-1814.
  20. [20]  Arefi, M., Firouzeh, S., Bidgoli, E.M.R., and Civalek, Ö. (2020), Analysis of porous micro-plates reinforced with FG-GNPs based on Reddy plate theory, Composite Structures, 247, 112391.
  21. [21]  Farajpour, A., Ghayesh, M.H., and Farokhi, H. (2018), A review on the mechanics of nanostructures, International Journal of Engineering Science, 133, 231-263.
  22. [22]  Caughey, T.K. (1963), Equivalent linearization techniques, The Journal of the Acoustical Society of America, 35(11), 1706-1711.
  23. [23]  Elishakoff, I., Fang, J., and Caimi, R. (1995), Random vibration of a nonlinearly deformed beam by a new stochastic linearization technique, International Journal of Solids and Structures, 32(11), 1571-1584.
  24. [24]  Elishakoff, I. and Andriamasy, L. (2010), Nonclassical linearization criteria in nonlinear stochastic dynamics, Journal of Applied Mechanics, 77(4), 044501.
  25. [25]  Zhang, X.T., Elishakoff, I., and Zhang, R,C, (1991), A stochastic linearization technique based on minimum mean square deviation of potential energies, In: Lin Y.K., Elishakoff I. (eds) Stochastic Structural Dynamics 1, Springer, Berlin, Heidelberg, https://doi.org/10.1007/978-3-642-84531-4\_17.
  26. [26]  Wang, C. and Zhang, X.T. (1985), An Improved Equivalent Linearization Technique in Nonlinear Random Vibration, Proceedings of the International Conference on Nonlinear Mechanics, 959-964.
  27. [27]  Anh, N.D., Hieu, N.N., and Linh, N.N. (2012), A dual criterion of equivalent linearization method for nonlinear systems subjected to random excitation, Acta Mechanica, 223(3), 645-654.
  28. [28]  Anh, N.D. and Linh, N.N. (2018), A weighted dual criterion of the equivalent linearization method for nonlinear systems subjected to random excitation, Acta Mechanica, 229, 1297-1310.
  29. [29]  Anh, N.D. and Di Paola, M. (1995), Some Extensions of Gaussian Equivalent Linearization, International Confernce on Nonlinear Stochastic Dynamics, Hanoi, Vietnam, 5-16.
  30. [30]  Elishakoff, I., Andriamasy, L., and Dolley, M. (2009), Application and extension of the stochastic linearization by Anh and Di Paola, Acta Mechanica, 204(1-2), 89-98.
  31. [31]  Anh, N.D., Elishakoff, I., and Hieu, N.N. (2014), Extension of the regulated stochastic linearization to beam vibrations, Probabilistic Engineering Mechanics, 35, 2-10.
  32. [32]  Crandall, S.H. and Yildiz, A. (1962), Random vibration of beams, Journal of Applied Mechanics, 29(2), 267-275.
  33. [33]  Hieu, N.N., Anh, N.D., and Hai, N.Q. (2016), Vibration analysis of beams subjected to random excitation by the dual criterion of equivalent linearization, Vietnam Journal of Mechanics, 38, 49-62.
  34. [34]  Spanos, P.D. and Malara, G. (2014), Nonlinear random vibrations of beams with fractional derivative elements, Journal of Engineering Mechanics, 140(9), 1-10.
  35. [35]  Burlon, A., Kougioumtzoglou, I.A., Failla, G., and Arena, F. (2019), Nonlinear random vibrations of beams with in-span supports via statistical linearization with constrained modes, Journal of Engineering Mechanics, 145(6), 04019038.
  36. [36]  Karimi, A.H. and Shadmani, M. (2019), Nonlinear vibration analysis of a beam subjected to a random axial force, Archive of Applied Mechanics, 89, 385-402.
  37. [37]  Rastehkenari, S.F. (2019), Random vibrations of functionally graded nanobeams based on unified nonlocal strain gradient theory, Microsystem Technologies, 25, 691-704.
  38. [38]  Rastehkenari, S.F. and Ghadiri, M. (2021), Nonlinear random vibrations of functionally graded porous nanobeams using equivalent linearization method, Applied Mathematical Modelling, 89, 1847-1859.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates