Advances in nano research

  • 제7권6호
  • /
  • Pages.391-403
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  • 2019
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  • 2287-237X(pISSN)
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  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Frequency response analysis of curved embedded magneto-electro-viscoelastic functionally graded nanobeams

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Fardshad, Ramin Ebrahimi (Department of Mechanical Engineering, Nitte Meenakshi Institute of Technology) ;
  • Mahesh, Vinyas (Department of Mechanical Engineering, Nitte Meenakshi Institute of Technology)
  • 투고 : 2019.04.03
  • 심사 : 2019.06.08
  • 발행 : 2019.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this article the frequency response analysis of curved magneto-electro-viscoelastic functionally graded (CMEV-FG) nanobeams resting on viscoelastic foundation has been carried out. To this end, the study incorporates the Euler-Bernoulli beam model in association with Eringen's nonlocal theory to incorporate the size effects. The viscoelastic foundation in the current investigation is assumed to be the combination of Winkler-Pasternak layer and viscous layer of infinite parallel dashpots. The equations of motion are derived with the aid of Hamilton's principle and the solution to vibration problem of CMEV-FG nanobeams are obtained analytically. The material gradation is considered to follow Power-law rule. This study thoroughly investigates the influence of prominent parameters such as linear, shear and viscous layers of foundation, structural damping coefficient, opening angle, magneto-electrical field, nonlocal parameter, power-law exponent and slenderness ratio on the frequencies of FG nanobeams.

키워드

참고문헌

  1. Akbas, S.D. (2018), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., Int. J., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039
  2. Altabey, W.A. (2017), "An exact solution for mechanical behavior of BFRP Nano-thin films embedded in NEMS", Adv. Nano Res., Int. J., 5(4), 337-357. https://doi.org/10.12989/anr.2017.5.4.337
  3. Assadi, A. and Farshi, B. (2011), "Size dependent vibration of curved nanobeams and rings including surface energies", Physica E: Low-dimens. Syst Nanostruct., 43(4), 975-978. https://doi.org/10.1016/j.physe.2010.11.031
  4. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimens. Syst. Nanostruct., 41(9), 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  5. Barati, M.R. (2017), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv. Nano Res., Int. J., 5(4), 393-414. https://doi.org/10.12989/anr.2017.5.4.393
  6. Barati, M.R., Zenkour, A.M. and Shahverdi, H. (2016), "Thermomechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory", Compos. Struct., 141, 203-212. https://doi.org/10.1016/j.compstruct.2016.01.056
  7. Beni, Y.T. (2016), "Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams", J. Intel. Mater. Syst. Struct., 27(16), 2199-2215. https://doi.org/10.1177/1045389X15624798
  8. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., Int. J., 3(1), 29-37. https://doi.org/10.12989/anr.2015.3.1.029
  9. Bhangale, R.K. and Ganesan, N. (2005), "Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells", J. Sound Vib., 288(1), 412-422. https://doi.org/10.1016/j.jsv.2005.04.008
  10. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147
  11. Castrucci, P. (2014), "Carbon nanotube/silicon hybrid heterojunctions for photovoltaic devices", Adv. Nano Res., Int. J., 2(1), 23-56. https://doi.org/10.12989/anr.2014.2.1.023
  12. Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A. A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., Int. J., 3(4), 193-206. https://doi.org/10.12989/anr.2015.3.4.193
  13. 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
  14. 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
  15. 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., 7(3), 119-143. https://doi.org/10.1080/19475411.2016.1223203
  16. Ebrahimi, F. and Barati, M.R. (2016d), "An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams", Adv. Nano Res., Int. J., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  17. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of smart size-dependent higher order magneto-electro-thermoelastic functionally graded nanosize beams", J. Mech., 33(1), 23-33. https://doi.org/10.1017/jmech.2016.46
  18. Ebrahimi, F. and Barati, M.R. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of sizedependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  19. Ebrahimi, F and Barati, M.R. (2017), "Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams", J. Mech., 33(1), 23-33 https://doi.org/10.1017/jmech.2016.46
  20. Ebrahimi, F. and Barati, M.R. (2018), "Stability analysis of functionally graded heterogeneous piezoelectric nanobeams based on nonlocal elasticity theory", Adv. Nano Res., Int. J., 6(2), 93-112. https://doi.org/10.12989/anr.2018.6.2.093
  21. 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/i2016-16160-1
  22. 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
  23. Ebrahimi, F. and Hosseini, S.H.S. (2016c), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Thermal Stress., 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  24. Ebrahimi, F. and Salari, E. (2015a), "Size-dependent thermoelectrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007
  25. 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
  26. 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
  27. 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", CMES: Comput. Model. Eng. Sci., 105, 151-181.
  28. 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
  29. 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
  30. 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
  31. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015a), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions", J. Thermal Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  32. Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015b), "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
  33. 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
  34. 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., Int. J., 5(2), 179-192. https://doi.org/10.12989/anr.2017.5.2.179
  35. Ehyaei, J., Akbarshahi, A. and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., Int. J., 5(2), 141-169. https://doi.org/10.12989/anr.2017.5.2.141
  36. Elmerabet, A.H., Heireche, H., Tounsi, A. and Semmah, A. (2017), "Buckling temperature of a single-walled boron nitride nanotubes using a novel nonlocal beam model", Adv. Nano Res., Int. J., 5(1), 1-12. https://doi.org/10.12989/anr.2017.5.1.001
  37. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Computat., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  38. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030
  39. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  40. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  41. Farhoudi, R. (2017), "An overview on recent new nano-antiparasitological findings and application", Adv. Nano Res., Int. J., 5(1), 49-59. https://doi.org/10.12989/anr.2017.5.1.049
  42. Hashemi, S.H., Mehrabani, H. and Ahmadi-Savadkoohi, A. (2015), "Exact solution for free vibration of coupled double viscoelastic graphene sheets by viscoPasternak medium", Compos. Part B: Eng., 78, 377-383. https://doi.org/10.1016/j.compositesb.2015.04.008
  43. Hosseini, M. and Jamalpoor, A. (2015), "Analytical solution for thermomechanical vibration of double-viscoelastic nanoplatesystems made of functionally graded materials", J. Thermal Stress., 38(12), 1428-1456. https://doi.org/10.1080/01495739.2015.1073986
  44. Hosseini, S.A.H. and Rahmani, O. (2016), "Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model", Appl. Phys. A, 122(3), 1-11. https://doi.org/10.1007/s00339-016-9696-4
  45. Huang, D.J., Ding, H.J. and Chen, W.Q. (2007), "Analytical solution for functionally graded magneto-electro-elastic plane beams", Int. J. Eng. Sci., 45(2), 467-485. https://doi.org/10.1016/j.ijengsci.2007.03.005
  46. Kananipour, H., Ahmadi, M. and Chavoshi, H. (2014), "Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams", Latin Am. J. Solids Struct., 11(5), 848-853. http://dx.doi.org/10.1590/S1679-78252014000500007
  47. Kattimani, S.C. and Ray, M.C. (2015), "Control of geometrically nonlinear vibrations of functionally graded magneto-electroelastic plates", Int. J. Mech. Sci., 99, 154-167. https://doi.org/10.1016/j.ijmecsci.2015.05.012
  48. Kheroubi, B., Benzair, A., Tounsi, A. and Semmah, A. (2016), "A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams", Adv. Nano Res., Int. J., 4(4), 251-264. https://doi.org/10.12989/anr.2016.4.4.251
  49. Lei, Y., Adhikari, S. and Friswell, M.I. (2013), "Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams", Int. J. Eng. Sci., 66, 1-13. https://doi.org/10.1016/j.ijengsci.2013.02.004
  50. Lezgy-Nazargah, M. and Cheraghi, N. (2015), "An exact Peano Series solution for bending analysis of imperfect layered FG neutral magneto-electro-elastic plates resting on elastic foundations", Mech. Adv. Mater. Struct., 24(3), 183-199. https://doi.org/10.1080/15376494.2015.1124951
  51. Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3), 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006
  52. Pouresmaeeli, S., Ghavanloo, E. and Fazelzadeh, S.A. (2013), "Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium", Compos. Struct., 96, 405-410. https://doi.org/10.1016/j.compstruct.2012.08.051
  53. Rahmani, O. and Jandaghian, A.A. (2015), "Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory", Appl. Phys. A, 119(3), 1019-1032. https://doi.org/10.1007/s00339-015-9061-z
  54. 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. Solids Struct., 12(10), 1901-1917. http://dx.doi.org/10.1590/1679-78251894
  55. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133, 368. https://doi.org/10.1140/epjp/i2018-12196-5
  56. She, G.L., Ren, Y.R. and Yan, K.M. (2019a), "On snap-buckling of porous FG curved nanobeams", Acta Astronautica, 161, 475-484. https://doi.org/10.1016/j.actaastro.2019.04.010
  57. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019b), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005
  58. Simsek, M. and Yurtcu, H.H. (2013), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  59. Sladek, J., Sladek, V., Krahulec, S., Chen, C.S. and Young, D.L. (2015), "Analyses of circular magnetoelectroelastic plates with functionally graded material properties", Mech. Adv. Mater. Struct., 22(6), 479-489. https://doi.org/10.1080/15376494.2013.807448
  60. Thai, H.T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. https://doi.org/10.1016/j.ijengsci.2011.11.011
  61. Tounsi, A., Benguediab, S., Adda, B., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  62. Tufekci, E., Aya, S.A. and Oldac, O. (2016), "In-plane static analysis of nonlocal curved beams with varying curvature and cross-section", Int. J. Appl. Mech., 8(1), 1650010. https://doi.org/10.1142/S1758825116500101
  63. Vinyas, M. (2019a), "Vibration control of skew magneto-electroelastic plates using active constrained layer damping", Compos. Struct., 208, 600-617. https://doi.org/10.1016/j.compstruct.2018.10.046
  64. Vinyas, M. (2019b), "A higher order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods", Compos. Part B, 158, 286-301. https://doi.org/10.1016/j.compositesb.2018.09.086
  65. Vinyas, M. and Kattimani, S.C. (2017a), "Static studies of stepped functionally graded magneto-electro-elastic beam subjected to different thermal loads", Compos. Struct., 163, 216-237. https://doi.org/10.1016/j.compstruct.2016.12.040
  66. Vinyas, M. and Kattimani, S.C. (2017b), "Static analysis of stepped functionally graded magneto-electro-elastic plates in thermal environment: A finite element study", Compos. Struct., 178, 63-86. https://doi.org/10.1016/j.compstruct.2017.06.068
  67. Vinyas, M. and Kattimani, S.C. (2017c), "Hygrothermal analysis of magneto-electro-elastic plate using 3D finite element analysis", Compos. Struct., 180, 617-637. https://doi.org/10.1016/j.compstruct.2017.08.015
  68. Vinyas, M. and Kattimani, S.C. (2018), "Finite element evaluation of free vibration characteristics of magneto-electro-elastic rectangular plates in hygrothermal environment using higherorder shear deformation theory", Compos. Struct., 202, 1339-1352. https://doi.org/10.1016/j.compstruct.2018.06.069
  69. Vinyas, M. and Kattimani, S. (2019), "Finite element simulation of controlled frequency response of skew multiphase magnetoelectro-elastic plates", J. Intel. Mater. Syst. Struct., 30(12), 1757-1771. https://doi.org/10.1177/1045389X19843674
  70. Vinyas, M, Kattimani, S.C., Loja, M.A.R. and Vishwas, M. (2018a), "Effect of $BaTiO_{3}/CoFe_{2}O_{4}$ micro-topological textures on the coupledstatic behaviour of magneto-electro-thermo-elastic beams indifferent thermal environment", Mater. Res. Express, 5, 125702. https://doi.org/10.1088/2053-1591/aae0c8
  71. Vinyas, M., Kattimani, S.C. and Joladarashi, S. (2018b), "Hygrothermal coupling analysis of magneto-electroelastic beams using finite element methods", J. Thermal Stress., 41(8), 1063-1079. https://doi.org/10.1080/01495739.2018.1447856
  72. Vinyas, M., Nischith, G., Loja, M.A.R., Ebrahimi, F. and Duc, N.D. (2019), "Numerical analysis of the vibration response of skew magneto-electro-elastic plates based on the higher-order shear deformation theory", Compos. Struct., 214, 132-142. https://doi.org/10.1016/j.compstruct.2019.02.010
  73. Wu, C.P. and Tsai, Y.H. (2007), "Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux", Int. J. Eng. Sci., 45(9), 744-769. https://doi.org/10.1016/j.ijengsci.2007.05.002
  74. Wu, C.P., Chen, S.J. and Chiu, K.H. (2010), "Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method", Mech. Res. Commun., 37(1), 54-60. https://doi.org/10.1016/j.mechrescom.2009.10.003
  75. Vinyas, M. (2019b), "A higher order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods", Compos. Part B: Eng., 158, 286-301. https://doi.org/10.1016/j.compositesb.2018.09.086
  76. 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(36), 365301. https://doi.org/10.1088/0022-3727/44/36/365301
  77. Youcef, D.O., Kaci, A., Houari, M.S.A., Tounsi, A., Benzair, A. and Heireche, H. (2015), "On the bending and stability of nanowire using various HSDTs", Adv. Nano Res., Int. J., 3(4), 177-191. https://doi.org/10.12989/anr.2015.3.4.177
  78. Zenkour, A.M. (2016), "Buckling of a single-layered graphene sheet embedded in visco-Pasternak's medium via nonlocal firstorder theory", Adv. Nano Res., Int. J., 4(4), 309-326. https://doi.org/10.12989/anr.2016.4.4.309

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