Structural Engineering and Mechanics

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Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment

  • Ebrahimi, Farzad (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University) ;
  • Daman, Mohsen (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University)
  • Received : 2017.06.04
  • Accepted : 2017.08.14
  • Published : 2017.10.10
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Abstract

This paper proposes an analytical solution method for free vibration of curved functionally graded (FG) nonlocal beam supposed to different thermal loadings, by considering porosity distribution via nonlocal elasticity theory for the first time. Material properties of curved FG beam are assumed to be temperature-dependent. Thermo-mechanical properties of porous FG curved beam are supposed to vary through the thickness direction of beam and are assumed to be temperature-dependent. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG structures. The rule of power-law is modified to consider influence of porosity according to even distribution. The governing equations of curved FG porous nanobeam under temperature field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is used to achieve the natural frequencies of porous FG curved nanobeam supposed to thermal loadings with simply supported boundary condition. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality, porosity volume fractions, type of temperature rising, gradient index, opening angle and aspect ratio of curved FG porous nanobeam on the natural frequency are successfully discussed. It is concluded that these parameters play key roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

Keywords

References

  1. Aissani, K., Bouiadjra, M.B., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., 55(4), 743-763. https://doi.org/10.12989/sem.2015.55.4.743
  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, 1439-1449. https://doi.org/10.1007/s00419-013-0756-3
  3. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of linearly tapered micro-columns based on strain gradient elasticity", Struct. Eng. Mech., 48(2), 195-205. https://doi.org/10.12989/sem.2013.48.2.195
  4. Berrabah, H. M., Tounsi, A., Semmah, A. and Adda, B. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351
  5. Bouderba, B., Houari, M. S. A., Tounsi, A. and Mahmoud, S. R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  6. Bousahla, A. A., Benyoucef, S., Tounsi, A. and Mahmoud, S. R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  7. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer Science & Business Media.
  8. Eltaher, M., Alshorbagy, A.E. and Mahmoud, F. (2013), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Model., 37, 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  9. Eltaher, M., Emam, S.A. and Mahmoud, F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Model., 218, 7406-7420.
  10. Ebrahimi, F. and Salari, E. (2015), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. Part B: Eng., 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  11. Ebrahimi, F. and Barati, M.R. (2016), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  12. Ebrahimi, F. and Barati, M.R. (2017a), "Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory", Mech. Adv. Mater. Struct., 1-10.
  13. Ebrahimi, F. and Barati, M.R. (2017b), "Vibration analysis of embedded size dependent FG nanobeams based on third-order shear deformation beam theory", Struct. Eng. Mech., 61(6), 721-736. https://doi.org/10.12989/sem.2017.61.6.721
  14. Ebrahimi, F. and Barati, M.R. (2017c), "Porosity-dependent vibration analysis of piezo-magnetically actuated heterogeneous nanobeams", Mech. Syst. Signal Pr., 93, 445-459. https://doi.org/10.1016/j.ymssp.2017.02.021
  15. Ebrahimi, F. and Barati, M.R. (2017d), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 24(11), 924-936. https://doi.org/10.1080/15376494.2016.1196795
  16. Ebrahimi, F. and Barati, M.R. (2017e), "A modified nonlocal couple stress based beam model for vibration analysis of higherorder FG nanobeams", Mech. Adv. Mater. Struct. (accepted)
  17. Ebrahimi, F. and Barati, M.R. (2017f), "Scale-dependent effects on wave propagation in magnetically affected single/doublelayered compositionally graded nanosize beams", Wave. Random Complex Media, 1-17.
  18. Ebrahimi, F. and Barati, M.R. (2017g), "Buckling analysis of nonlocal strain gradient axially functionally graded nanobeams resting on variable elastic medium", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 0954406217713518.
  19. Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronautica, 116, 117-125. https://doi.org/10.1016/j.actaastro.2015.06.014
  20. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51, 223-249. https://doi.org/10.1007/s11012-015-0208-y
  21. Ebrahimi, F. and Jafari, A. (2016a), "Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59, 343-371. https://doi.org/10.12989/sem.2016.59.2.343
  22. Ebrahimi, F. and Jafari, A. (2016b), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 2016, Article ID 9561504, 20.
  23. Ebrahimi, F. and Daman, M. (2016), "Investigating surface effects on thermomechanical behavior of embedded circular curved nanosize beams", J. Eng., 2016, Article ID 9848343, 11.
  24. Ebrahimi, F. and Daman, M. (2016), "An investigation of radial vibration modes of embedded double-curved-nanobeamsystems", Cankaya Univ. J. Sci. Eng., 13, 58-79.
  25. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H., Shaghaghi, G.R. (2015), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Technol., 29, 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  26. Ebrahimi, F. and Barati, M.R. (2016b), "Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams", Euro. Phys. J. Plus, 131, 346. https://doi.org/10.1140/epjp/i2016-16346-5
  27. Ebrahimi, F. and Shaghaghi, G.R. (2016), "Thermal effects on nonlocal vibrational characteristics of nanobeams with nonideal boundary conditions", Smart Struct. Syst., 18(6), 1087-1109. https://doi.org/10.12989/sss.2016.18.6.1087
  28. Ebrahimi, F. and Dabbagh, A. (2017), "Wave propagation analysis of smart rotating porous heterogeneous piezo-electric nanobeams", Euro. Phys. J. Plus, 132(4), 153. https://doi.org/10.1140/epjp/i2017-11366-3
  29. Ebrahimi, F. and Salari, E. (2016a), "Analytical modeling of dynamic behavior of piezo-thermo-electrically affected sigmoid and power-law graded nanoscale beams", Appl. Phys. A, 122(9), 793. https://doi.org/10.1007/s00339-016-0273-7
  30. Ebrahimi, F. and Salari, E. (2016b), "Thermal loading effects on electro-mechanical vibration behavior of piezoelectrically actuated inhomogeneous size-dependent Timoshenko nanobeams", Adv. Nano Res., 4(3), 197-228. https://doi.org/10.12989/anr.2016.4.3.197
  31. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringens nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837
  32. Ehyaei, J. and Daman, M. (2017), "Free vibration analysis of double walled carbon nanotubes embedded in an elastic medium with initial imperfection", Adv. Nano Res., 5(2), 179-192. https://doi.org/10.12989/ANR.2017.5.2.179
  33. Hosseini, S. and Rahmani, O. (2016), "Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model", Appl. Phys. A, 122, 1-11.
  34. Kocaturk, T. and Akbas, S.D. (2013), "Wave propagation in a microbeam based on the modified couple stress theory", Struct. Eng. Mech., 46(3), 417-431. https://doi.org/10.12989/sem.2013.46.3.417
  35. Kananipour, H., Ahmadi, M. and Chavoshi, H. "Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams", Latin Am. J. Solid. Struct., 11, 848-853, 2014. https://doi.org/10.1590/S1679-78252014000500007
  36. Malekzadeh, P., Haghighi, M.G. and Atashi, M. (2010), "Out-ofplane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct., 92, 541-552. https://doi.org/10.1016/j.compstruct.2009.08.040
  37. Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B.B. (2010), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Brazil. Soc. Mech. Sci. Eng., 38(8), 2193-2211.
  38. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (2013), Functionally Graded Materials: Design, Processing and Applications, Springer Science & Business Media.
  39. Nazemnezhad, R. and Hosseini-Hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199. https://doi.org/10.1016/j.compstruct.2013.12.006
  40. Pour, H.R., Vossough, H., Heydari, M.M., Beygipoor, G. and Azimzadeh, A. (2015), "Nonlinear vibration analysis of a nonlocal sinusoidal shear deformation carbon nanotube using differential quadrature method", Struct. Eng. Mech., 54(6), 1061-1073. https://doi.org/10.12989/sem.2015.54.6.1061
  41. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  42. Setoodeh, A., Derahaki, M. and Bavi, N. (2015), "DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory", Latin Am. J. Solid. Struct., 12, 1901-1917. https://doi.org/10.1590/1679-78251894
  43. Shen, H.S. (2016), Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press.
  44. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., 60(4), 547-565. https://doi.org/10.12989/sem.2016.60.4.547
  45. Taghizadeh, M., Ovesy, H.R. and Ghannadpour, S.A.M. (2015), "Nonlocal integral elasticity analysis of beam bending by using finite element method", Struct. Eng. Mech., 54(4), 755-769. https://doi.org/10.12989/sem.2015.54.4.755
  46. Touloukian, Y.S. (1966), "Thermophysical properties of high temperature solid materials, Volume 6, intermetallics, cermets, polymers, and composite systems, Part II. cermets, polymers, composite systems", Dtic Document.
  47. Wang, C.M. and Duan, W. (2008), "Free vibration of nanorings/arches based on nonlocal elasticity", J. Appl. Phys., 104, 014303. https://doi.org/10.1063/1.2951642
  48. Wattanasakulpong, N., Prusty, B. G., Kelly, D. W. and Hoffman, M. "Free vibration analysis of layered functionally graded beams with experimental validatio", Mater. Des., 36, 182-190.
  49. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32, 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  50. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory", Chebyshev Coll. Meth., Meccanica, 50, 1331-1342.
  51. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53, 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  52. Yan, Z. and Jiang, L. (2011), "Electromechanical response of a curved piezoelectric nanobeam with the consideration of surface effects", J. Phys. D: Appl. Phys., 44, 365301. https://doi.org/10.1088/0022-3727/44/36/365301
  53. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693
  54. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO 2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68, 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2

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