Steel and Composite Structures

  • 제28권2호
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  • Pages.149-165
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  • 2018
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Nonlinear free and forced vibration analysis of microbeams resting on the nonlinear orthotropic visco-Pasternak foundation with different boundary conditions

  • 투고 : 2017.06.08
  • 심사 : 2018.05.24
  • 발행 : 2018.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

Using the modified couple stress theory and Euler-Bernoulli beam theory, this paper studies nonlinear vibration analysis of microbeams resting on the nonlinear orthotropic visco-Pasternak foundation. Using the Hamilton's principle, the set of the governing equations are derived and solved numerically using differential quadrature method (DQM), Newark beta method and arc-length technique for all kind of the boundary conditions. First convergence and accuracy of the presented solution are demonstrated and then effects of radius of gyration, Poisson's ratio, small scale parameters, temperature changes and coefficients of the foundation on the linear and nonlinear natural frequencies and dynamic response of the microbeam are investigated.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  2. Azrar, L., Benamar, R. and White, R. (1999), "Semi-analytical approach to the non-linear dynamic response problem of S-S and C-C beams at large vibration amplitudes part I: General theory and application to the single mode approach to free and forced vibration analysis", J. Sound Vib., 224(2), 183-207. https://doi.org/10.1006/jsvi.1998.1893
  3. Bellman, R. and Roth, R.S. (1979), "Systems identification with partial information", J. Math. Anal. Appl., 68(2), 321-333. https://doi.org/10.1016/0022-247X(79)90120-3
  4. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: a review", Appl. Mech. Rev., 49, 1-28. https://doi.org/10.1115/1.3101882
  5. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  6. Farokhi, H. and Ghayesh, M.H. (2015), "Thermo-mechanical dynamics of perfect and imperfect Timoshenko microbeams", Int. J. Eng. Sci., 91, 12-33. https://doi.org/10.1016/j.ijengsci.2015.02.005
  7. Farokhi, H. and Ghayesh, M.H. (2017), "Viscoelasticity effects on resonant response of a shear deformable extensible microbeam", Nonlinear Dyn., 87(1), 391-406. https://doi.org/10.1007/s11071-016-3050-4
  8. Ghayesh, M.H. and Amabili, M. (2014), "Coupled longitudinaltransverse behaviour of a geometrically imperfect microbeam", Compos. Part B: Eng., 60, 371-377. https://doi.org/10.1016/j.compositesb.2013.12.030
  9. Ghayesh, M.H. and Farokhi, H. (2015), "Coupled longitudinaltransverse-rotational behaviour of shear deformable microbeams", Compos. Part B: Eng., 77, 319-328. https://doi.org/10.1016/j.compositesb.2015.03.032
  10. Ghayesh, M.H., Farokhi, H. and Amabili, M. (2013), "Nonlinear dynamics of a microscale beam based on the modified couple stress theory", Compos. Part B: Eng., 50, 318-324. https://doi.org/10.1016/j.compositesb.2013.02.021
  11. Ghayesh, M.H., Farokhi, H. and Amabili, M. (2014), "In-plane and out-of-plane motion characteristics of microbeams with modal interactions", Compos. Part B: Eng., 60, 423-439 https://doi.org/10.1016/j.compositesb.2013.12.074
  12. Ghayesh, M.H., Farokhi, H. and Gholipour, A. (2017), "Oscillations of functionally graded microbeams", Int. J. Eng. Sci., 110, 35-53. https://doi.org/10.1016/j.ijengsci.2016.09.011
  13. Ghorbanpour Arani, A., Mohammadimehr, M., Arefmanesh, A. and Ghasemi, A. (2010), "Transverse vibration of short carbon nanotubes using cylindrical shell and beam models", Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 224(3), 745-756. https://doi.org/10.1243/09544062JMES1659
  14. Ghorbanpour Arani, A. and Shokravi, M. (2013), "Nonlocal vibration behavior of a viscoelastic SLGS embedded on visco-Pasternak foundation under magnetic field", J. Nanostruct., 3(4), 467-476.
  15. Ghorbanpour Arani, A., Kolahchi, R., Vossough, H. and Abdollahian, M. (2013), "Vibration and stability analysis of a Pasternak bonded double-GNR-system based on different nonlocal theories", J. Solid Mech., 5(1), 92-106.
  16. Gurtin, M.E. and Ian Murdoch, A. (1975), "A continuum theory of elastic material surfaces", Arch. Rational Mech. Anal., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  17. Jia, X.L., Ke, L.L., Feng, C.B., Yang, J. and Kitipornchai, S. (2015), "Size effect on the free vibration of geometrically nonlinear functionally graded micro-beams under electrical actuation and temperature change", Compos. Struct., 133, 1137-1148. https://doi.org/10.1016/j.compstruct.2015.08.044
  18. Kahrobaiyan, M., Rahaeifard, M., Tajalli, S. and Ahmadian, M. (2012), "A strain gradient functionally graded Euler-Bernoulli beam formulation", Int. J. Eng. Sci., 52, 65-76. https://doi.org/10.1016/j.ijengsci.2011.11.010
  19. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Nonlinear free vibration of size-dependent functionally graded microbeams", Int. J. Eng. Sci., 50(1), 256-267. https://doi.org/10.1016/j.ijengsci.2010.12.008
  20. Kong, S., Zhou, S., Nie, Z. and Wang, K. (2008), "The sizedependent natural frequency of Bernoulli-Euler microbeams", Int. J. Eng. Sci., 46(5), 427-437. https://doi.org/10.1016/j.ijengsci.2007.10.002
  21. Kuang, J.H. and Chen, C.J. (2004), "Dynamic characteristics of shaped micro-actuators solved using the differential quadrature method", J. Micromech. Microeng., 14(4), 647-655. https://doi.org/10.1088/0960-1317/14/4/028
  22. Lam, D.C., Yang, F., Chong, A., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  23. Lyshevski, S.E. (2002), MEMS and NEMS: Systems, Devices, and Structures, (1th Edition), CRC press, New York, NY, USA.
  24. Ma, H., Gao, X.L. and Reddy, J. (2010), "A nonclassical Reddy-Levinson beam model based on a modified couple stress theory", Int. J. Multiscale Computat. Eng., 8(2), 217-235.
  25. Mohammadimehr, M. and Shahedi, S. (2016), "Nonlinear magneto-electro-mechanical vibration analysis of doublebonded sandwich Timoshenko microbeams based on MSGT using GDQM", Steel Compos. Struct., Int. J., 21(1), 1-36. https://doi.org/10.12989/scs.2016.21.1.001
  26. Mohammadimehr, M., Rostami, R. and Arefi, M. (2016), "Electroelastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., Int. J., 20(3), 513-543. https://doi.org/10.12989/scs.2016.20.3.513
  27. Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. Div., 85(3), 67-94.
  28. Park, W.T., Han, S.C., Jung, W.Y. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., Int. J., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239
  29. 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
  30. Rashvand, K., Rezazadeh, G., Mobki, H. and Ghayesh, M.H. (2013), "On the size-dependent behavior of a capacitive circular micro-plate considering the variable length-scale parameter", Int. J. Mech. Sci., 77, 333-342. https://doi.org/10.1016/j.ijmecsci.2013.09.023
  31. Rahmani, O., Refaeinejad, V. and Hosseini, S.A.H. (2017), "Assessment of various nonlocal higher order theories for the bending and buckling behavior of functionally graded nanobeams", Steel Compos. Struct., Int. J., 23(3), 339-350. https://doi.org/10.12989/scs.2017.23.3.339
  32. Rao, S.S. (2007), Vibration of Continuous Systems, John Wiley & Sons, New Jersey, Inc., USA.
  33. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons, New Jersey, Inc., USA.
  34. Roque, C., Fidalgo, D., Ferreira, A. and Reddy, J. (2013), "A study of a microstructure-dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method", Compos. Struct., 96, 532-537. https://doi.org/10.1016/j.compstruct.2012.09.011
  35. Sahmani, S., Bahrami, M., Aghdam, M. and Ansari, R. (2014), "Surface effects on the nonlinear forced vibration response of third-order shear deformable nanobeams", Compos. Struct., 118, 149-158. https://doi.org/10.1016/j.compstruct.2014.07.026
  36. Simsek, M. (2011), "Forced vibration of an embedded singlewalled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory", Steel Compos. Struct., Int. J., 11(1), 59-76. https://doi.org/10.12989/scs.2011.11.1.059
  37. 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., 112, 264-272. https://doi.org/10.1016/j.compstruct.2014.02.010
  38. Stolken, J. and Evans, A. (1998), "A microbend test method for measuring the plasticity length scale", Acta Materialia, 46(14), 5109-5115. https://doi.org/10.1016/S1359-6454(98)00153-0
  39. Tagrara, S.H., Benachour, A., Bouiadjra, M.B. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., Int. J., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259
  40. Tilmans, H.A. and Legtenberg, R. (1994), "Electrostatically driven vacuum-encapsulated polysilicon resonators: Part II. Theory and performance", Sensor. Actuat. A: Phys., 45(1), 67-84. https://doi.org/10.1016/0924-4247(94)00813-2
  41. Wang, Y.G., Lin, W.H. and Liu, N. (2013), "Nonlinear free vibration of a microscale beam based on modified couple stress theory", Physica E: Low-dimensional Syst. Nanostruct., 47, 80-85. https://doi.org/10.1016/j.physe.2012.10.020
  42. Yang, F., Chong, A.C., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  43. Yang, J., Hu, Y. and Kitipornchai, S. (2012), "Electro-dynamic behavior of an electrically actuated micro-beam: Effects of initial curvature and nonlinear deformation", Comput. Struct., 96, 25-33.
  44. Zhong, H. and Guo, Q. (2003), "Nonlinear vibration analysis of Timoshenko beams using the differential quadrature method", Nonlinear Dyn., 32(3), 223-234. https://doi.org/10.1023/A:1024463711325

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