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Free vibration of deep curved FG nano-beam based on modified couple stress theory

  • Rahmani, O. (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan) ;
  • Hosseini, S.A.H. (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan) ;
  • Ghoytasi, I. (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan) ;
  • Golmohammadi, H. (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan)
  • Received : 2017.06.05
  • Accepted : 2017.12.22
  • Published : 2018.03.10
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Abstract

Vibration analysis of deep curved FG nano-beam has been carried out based on modified couple stress theory. Material properties of curved Timoshenko beam are assumed to be functionally graded in radial direction. Governing equations of motion and related boundary conditions have been obtained via Hamilton's principle. In a parametric study, influence of length scale parameter, aspect ratio, gradient index, opening angle, mode number and interactive influences of these parameters on natural frequency of the beam, have been investigated. It was found that, considering geometrical deepness term leads to an increase in sensitivity of natural frequency about variation of aforementioned parameters.

Keywords

References

  1. Akgoz, B. and Civalek, O. (2013), "Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory", Compos. Struct., 98, 314-322. https://doi.org/10.1016/j.compstruct.2012.11.020
  2. Ansari, R., Gholami, R. and Sahmani, S. (2013), "Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory", Arch. Appl. Mech., 83(10), 1439-1449. https://doi.org/10.1007/s00419-013-0756-3
  3. Arbind, A. and Reddy, J.N. (2013), "Nonlinear analysis of functionally graded microstructure-dependent beams", Compos. Struct., 98, 272-281. https://doi.org/10.1016/j.compstruct.2012.10.003
  4. Asghari, M., Kahrobaiyan, M. and Ahmadian, M. (2010), "A nonlinear Timoshenko beam formulation based on the modified couple stress theory", Int. J. Eng. Sci., 48(12), 1749-1761. https://doi.org/10.1016/j.ijengsci.2010.09.025
  5. Chong, A. and Lam, D.C. (1999), "Strain gradient plasticity effect in indentation hardness of polymers", J. Mater. Res., 14(10), 4103-4110. https://doi.org/10.1557/JMR.1999.0554
  6. Darabi, M., Darvizeh, M. and Darvizeh, A. (2008), "Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading", Compos. Struct., 83(2), 201-211. https://doi.org/10.1016/j.compstruct.2007.04.014
  7. Ebrahimi, F. and Daman, M. (2016), "Dynamic modeling of embedded curved nanobeams incorporating surface effects", Coupled Syst. Mech., Int. J., 5(3), 255-267. https://doi.org/10.12989/csm.2016.5.3.255
  8. Ebrahimi, F. and Daman, M. (2017), "Analytical investigation of the surface effects on nonlocal vibration behavior of nanosize curved beams", Adv. Nano Res., Int. J., 5(1), 35-47. https://doi.org/10.12989/anr.2017.5.1.035
  9. Fereidoon, A., Andalib, M. and Hemmatian, H. (2015), "Bending Analysis of Curved Sandwich Beams with Functionally Graded Core", Mech. Adv. Mater. Struct., 22(7), 564-577. https://doi.org/10.1080/15376494.2013.828815
  10. Hajianmaleki, M. and Qatu, M.S. (2012), "Static and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions", Compos. Part B: Eng., 43(4), 1767-1775. https://doi.org/10.1016/j.compositesb.2012.01.019
  11. Hosseini, S. and Rahmani, O. (2016a), "Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model", Appl. Phys. A, 122(3), 1-11.
  12. Hosseini, S. and Rahmani, O. (2016b), "Surface effects on buckling of double nanobeam system based on nonlocal Timoshenko model", Int. J. Struct. Stabil. Dyn., 16(10),1550077. https://doi.org/10.1142/S0219455415500777
  13. Hosseini, S.A.H. and Rahmani, O. (2016c), "Thermomechanical vibration of curved functionally graded nanobeam based on nonlocal elasticity", J. Therm. Stress., 1-16.
  14. Jandaghian, A.A. and Rahmani, O. (2015), "On the buckling behavior of piezoelectric nanobeams: An exact solution", J. Mech. Sci. Technol., 29(8), 3175-3182. https://doi.org/10.1007/s12206-015-0716-7
  15. Jandaghian, A.A. and Rahmani, O. (2016), "An Analytical Solution for Free Vibration of Piezoelectric Nanobeams Based on a Nonlocal Elasticity Theory", J. Mech., 32(2), 143-151. https://doi.org/10.1017/jmech.2015.53
  16. Jomehzadeh, E., Noori, H. and Saidi, A. (2011), "The sizedependent vibration analysis of micro-plates based on a modified couple stress theory", Physica E: Low-dimens. Syst. Nanostruct., 43(4), 877-883. https://doi.org/10.1016/j.physe.2010.11.005
  17. Lam, D., 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
  18. Lanhe, W., Hongjun, W. and Daobin, W. (2007), "Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method", Compos. Struct., 77(3), 383-394. https://doi.org/10.1016/j.compstruct.2005.07.011
  19. Liu, Y. and Reddy, J. (2011), "A nonlocal curved beam model based on a modified couple stress theory", Int. J. Struct. Stabil. Dyn., 11(3), 495-512. https://doi.org/10.1142/S0219455411004233
  20. Ma, H., Gao, X.-L. and Reddy, J. (2008), "A microstructuredependent Timoshenko beam model based on a modified couple stress theory", J. Mech. Phys. Solids, 56(12), 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007
  21. Ma, H., Gao, X.-L. and Reddy, J. (2011), "A non-classical Mindlin plate model based on a modified couple stress theory", Acta Mechanica, 220(1-4), 217-235. https://doi.org/10.1007/s00707-011-0480-4
  22. McFarland, A.W. and Colton, J.S. (2005), "Role of material microstructure in plate stiffness with relevance to microcantilever sensors", J. Micromech. Microeng., 15(5), 1060. https://doi.org/10.1088/0960-1317/15/5/024
  23. Mohammad-Abadi, M. and Daneshmehr, A. (2014), "Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundary conditions", Int. J. Eng. Sci., 74, 1-14. https://doi.org/10.1016/j.ijengsci.2013.08.010
  24. Nateghi, A., Salamat-talab, M., Rezapour, J. and Daneshian, B. (2012), "Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory", Appl. Math. Model., 36(10), 4971-4987. https://doi.org/10.1016/j.apm.2011.12.035
  25. Nie, G. and Zhong, Z. (2012), "Exact Solutions for Elastoplastic Stress Distribution in Functionally Graded Curved Beams Subjected to Pure Bending", Mech. Adv. Mater. Struct., 19(6), 474-484. https://doi.org/10.1080/15376494.2011.556835
  26. Park, S. and Gao, X. (2006), "Bernoulli-Euler beam model based on a modified couple stress theory", J. Micromech. Microeng., 16(11), 2355. https://doi.org/10.1088/0960-1317/16/11/015
  27. Park, S.K. and Gao, X.L. (2008a), "Micromechanical Modeling of Honeycomb Structures Based on a Modified Couple Stress Theory", Mech. Adv. Mater. Struct., 15(8), 574-593. https://doi.org/10.1080/15376490802470499
  28. Park, S. and Gao, X.-L. (2008b), "Variational formulation of a modified couple stress theory and its application to a simple shear problem", Zeitschrift fur angewandte Mathematik und Physik, 59(5), 904-917. https://doi.org/10.1007/s00033-006-6073-8
  29. Qatu, M.S. (2004), Vibration of Laminated Shells and Plates, Elsevier.
  30. Rahmani, O., Hosseini, S.A.H. and Hayati, H. (2016), "Frequency analysis of curved nano-sandwich structure based on a nonlocal model", Modern Phys. Lett. B, 30(10), 1650136.
  31. Roque, C., Ferreira, A. and Jorge, R. (2007), "A radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory", J. Sound Vib., 300(3), 1048-1070. https://doi.org/10.1016/j.jsv.2006.08.037
  32. Salamat-talab, M., Nateghi, A. and Torabi, J. (2012), "Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory", Int. J. Mech. Sci., 57(1), 63-73. https://doi.org/10.1016/j.ijmecsci.2012.02.004
  33. Shafiei, N., Kazemi, M. and Fatahi, L. (2015), "Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method", Mech. Adv. Mater. Struct., 24(3), 240-252.
  34. Shariat, B.S. and Eslami, M. (2007), "Buckling of thick functionally graded plates under mechanical and thermal loads", Compos. Struct., 78(3), 433-439. https://doi.org/10.1016/j.compstruct.2005.11.001
  35. Simsek, M., Kocaturk, T. and Akbas, S.D. (2013), "Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory", Compos. Struct., 95, 740-747. https://doi.org/10.1016/j.compstruct.2012.08.036
  36. Simsek, M. and Reddy, J. (2013), "Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory", Int. J. Eng. Sci., 64, 37-53. https://doi.org/10.1016/j.ijengsci.2012.12.002
  37. Thai, H.-T. and Choi, D.-H. (2013), "Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory", Compos. Struct., 95, 142-153. https://doi.org/10.1016/j.compstruct.2012.08.023
  38. Tsiatas, G.C. (2009), "A new Kirchhoff plate model based on a modified couple stress theory", Int. J. Solids Struct., 46(13), 2757-2764. https://doi.org/10.1016/j.ijsolstr.2009.03.004
  39. Xia, W., Wang, L. and Yin, L. (2010), "Nonlinear non-classical microscale beams: static bending, postbuckling and free vibration", Int. J. Eng. Sci., 48(12), 2044-2053. https://doi.org/10.1016/j.ijengsci.2010.04.010
  40. Yang, F., Chong, A., Lam, D. 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
  41. Zand, M.M. (2012), "The dynamic pull-in instability and snapthrough behavior of initially curved microbeams", Mech. Adv. Mater. Struct., 19(6), 485-491. https://doi.org/10.1080/15376494.2011.556836

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