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Vibration analysis of inhomogeneous nonlocal beams via a modified couple stress theory incorporating surface effects

  • Ebrahimi, Farzad (Mechanical Engineering department, faculty of engineering, Imam Khomeini International University) ;
  • Safarpour, Hamed (Mechanical Engineering department, faculty of engineering, Imam Khomeini International University)
  • Received : 2017.08.08
  • Accepted : 2018.02.08
  • Published : 2018.12.25
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Abstract

This paper presents a free vibration analysis of size-dependent functionally graded (FG) nanobeams with all surface effects considerations on the basis of modified couple stress theory. The material properties of FG nanobeam are assumed to vary according to power law distribution. Based on the Euler-Bernoulli beam theory, the modeled nanobeam and its equations of motion are derived using Hamilton's principle. An analytical method is used to discretize the model and the equation of motion. The model is validated by comparing the benchmark results with the obtained results. Results show that the vibration behavior of a nanobeam is significantly influenced by surface density, surface tension and surface elasticity. Also, it is shown that by increasing the beam size, influence of surface effect reduces to zero, and the natural frequency tends to its classical value.

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References

  1. Abdelhak, Z., Hadji, L., Khelifa, Z., Hassaine, D. and Adda Bedia, E.A. (2016), "Analysis of buckling response of functionally graded sandwich plates using a refined shear deformation theory", Wind Struct., 22(3), 130-141.
  2. Abdelaziz et al. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/SCS.2017.25.6.693
  3. Asghari, M. et al. (2011), "Investigation of the size effects in Timoshenko beams based on the couple stress theory", Arch. Appl. Mech., 81(7), 863-874. https://doi.org/10.1007/s00419-010-0452-5
  4. Bouderba, B. et al. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  5. Chen, L. et al. (2012), "Engineering controllable bidirectional molecular motors based on myosin", Nat. Nano, 7(4), 252-256. https://doi.org/10.1038/nnano.2012.19
  6. Chen, T., Chiu, M.S. and Weng, C.N. (2006), "Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids", J. Appl. Phys., 100(7), 074308. https://doi.org/10.1063/1.2356094
  7. Chong, A. et al. (2001), "Torsion and bending of micron-scaled structures", J. Mater. Res., 16(4), 1052-1058. https://doi.org/10.1557/JMR.2001.0146
  8. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Tech., 29, 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  9. Ebrahimi, F. and Salari, E. (2015a), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007, 2015 https://doi.org/10.1088/0964-1726/24/12/125007
  10. Ebrahimi, F. and Salari, E. (2015b), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronautica, 113, 29-50. https://doi.org/10.1016/j.actaastro.2015.03.031
  11. Ebrahimi, F. and Salari, E. (2015c), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. B, 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  12. Ebrahimi, F. and Salari, E. (2015d), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", Comput. Model. Eng. Sci., 105, 151-181.
  13. Ebrahimi, F. and Salari, E. (2015e), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. https://doi.org/10.1016/j.compstruct.2015.03.023
  14. Ebrahimi, F. and Salari, E. (2015f), "Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions", Compos. B, 78, 272-290. https://doi.org/10.1016/j.compositesb.2015.03.068
  15. Ebrahimi, F. and Salari, E. (2016), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams", Mech. Adv. Mater. Struct., 23(12), 1379-1397. https://doi.org/10.1080/15376494.2015.1091524
  16. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions", J. Therm. Stresses, 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  17. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2016), "In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams", Meccanica, 51(4), 951-977. https://doi.org/10.1007/s11012-015-0248-3
  18. Ebrahimi, F. and Barati, M.R. (2016a), "Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams", Eur. Phys. J. Plus, 131(9), 346. https://doi.org/10.1140/epjp/i2016-16346-5
  19. Ebrahimi, F. and Barati, M.R. (2016b), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  20. Ebrahimi, F. and Barati, M.R. (2016c), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", Int. J. Smart Nano Mater., 1-25.
  21. Ebrahimi, F. and Barati, M.R. (2016d), "An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams", Adv. Nano Res., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  22. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams", J. Mech., 1-11.
  23. Ebrahimi, F. and Barati, M.R. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of sizedependent functionally graded nanobeams", Arabian J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  24. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Double nanoplatebased NEMS under hydrostatic and electrostatic actuations", Eur. Phys. J. Plus, 131(5), 1-19. https://doi.org/10.1140/epjp/i2016-16001-3
  25. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Nonlinear electroelastic vibration analysis of NEMS consisting of doubleviscoelastic nanoplates", Appl. Phys. A, 122(10), 922. https://doi.org/10.1007/s00339-016-0452-6
  26. Ebrahimi, F. and Hosseini, S.H.S. (2016c), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stresses, 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  27. Ebrahimi, F. and Nasirzadeh, P. (2015), "A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method", J. Theor. Appl. Mech., 53(4), 1041-1052.
  28. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size dependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  29. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. An., 57(4), 291-323. https://doi.org/10.1007/BF00261375
  30. Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solids Struct., 14(6), 431-440. https://doi.org/10.1016/0020-7683(78)90008-2
  31. Gurtin, M.E., Weissmuller, J. and Larche, F. (1998), "A general theory of curved deformable interfaces in solids at equilibrium", Philos. Magazine A, 78(5), 1093-1109. https://doi.org/10.1080/014186198253138
  32. Khanade K., Sasangohar, F., Sadeghi, M., Sutherland, S. and Alexander, K. (2015), "Deriving information requirements for a smart nursing system for intensive care units", Proceedings of the Human Factors and Ergonomics Society Annual Meeting.
  33. Kong, S. et al. (2008), "The size-dependent natural frequency of Bernoulli-Euler micro-beams", Int. J. Eng. Sci., 46(5), 427-437. https://doi.org/10.1016/j.ijengsci.2007.10.002
  34. Lee, Z. et al. (2006), "Metallic NEMS components fabricated from nanocomposite Al-Mo films", Nanotechnology, 17(12), 3063. https://doi.org/10.1088/0957-4484/17/12/042
  35. Lei, X.W. et al. (2012), "Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model", Compos. Part B: Eng., 43(1), 64-69. https://doi.org/10.1016/j.compositesb.2011.04.032
  36. Li, J. et al. (2014), "Rotation motion of designed nano-turbine", Sci. Rep., 4.
  37. Lu, P. et al. (2006), "Dynamic properties of flexural beams using a nonlocal elasticity model", J. Appl. Phys., 2006. 99(7).
  38. Lu, C., Lim, C.W. and Chen, W. (2009), "Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory", Int. J. Solids Struct., 46(5), 1176-1185. https://doi.org/10.1016/j.ijsolstr.2008.10.012
  39. Natarajan, S. et al. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031
  40. Nateghi, A. and Salamat-talab, M. (2013), "Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory", Compos. Struct., 96, 97-110. https://doi.org/10.1016/j.compstruct.2012.08.048
  41. Rahaeifard, M., Kahrobaiyan, M. and Ahmadian, M. (2009), "Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials", Proceedings of the ASME 2009 international design engineering technical conferences and computers and information in engineering conference, American Society of Mechanical Engineers.
  42. Reddy, J. (2011), "Microstructure-dependent couple stress theories of functionally graded beams", J. Mech. Phys. Solids, 59(11), 2382-2399. https://doi.org/10.1016/j.jmps.2011.06.008
  43. Sadeghi M., Thomassie, R. and Sasangohar, F. (2017), "Objective assessment of functional information requirements for patient portals", Proceedings of the Human Factors and Ergonomics Society Annual Meeting.
  44. Shaat, M. et al. (2014), "Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects", Int. J. Mech. Sci., 79, 31-37. https://doi.org/10.1016/j.ijmecsci.2013.11.022
  45. Tauchert, T.R. (1974), Energy principles in structural mechanics, McGraw-Hill Companies.
  46. Toupin, R.A. (1962), "Elastic materials with couple-stresses", Arch. Ration. Mech. An., 11(1), 385-414. https://doi.org/10.1007/BF00253945
  47. Vafamehr, A. et al. (2017), "A framework for expansion planning of data centers in electricity and data networks under uncertainty", IEEE T. Smart Grid.
  48. Wang, G.F. and Feng, X.Q. (2007), "Effects of surface elasticity and residual surface tension on the natural frequency of microbeams", Appl. Phys. Lett., 90(23), 231904. https://doi.org/10.1063/1.2746950
  49. Witvrouw, A. and Mehta, A. (2005), The use of functionally graded poly-SiGe layers for MEMS applications. in Materials science forum, Trans Tech Publ.
  50. Yang, F. et al. (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
  51. Yan, Z. and Jiang, L. (2011), "The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects", Nanotechnology, 22(24), 245703. https://doi.org/10.1088/0957-4484/22/24/245703

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