Coupled systems mechanics

  • 제7권4호
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  • Pages.373-393
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  • 2018
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

A nonlocal strain gradient theory for scale-dependent wave dispersion analysis of rotating nanobeams considering physical field effects

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Haghi, Parisa (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2017.12.28
  • 심사 : 2018.01.05
  • 발행 : 2018.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper is concerned with the wave propagation behavior of rotating functionally graded temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field. Uniform, linear and nonlinear temperature distributions across the thickness are investigated. Thermo-elastic properties of FG beam change gradually according to the Mori-Tanaka distribution model in the spatial coordinate. The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function. The governing equations are derived by Hamilton's principle as a function of axial force due to centrifugal stiffening and displacement. By applying an analytical solution and solving an eigenvalue problem, the dispersion relations of rotating FG nanobeam are obtained. Numerical results illustrate that various parameters including temperature change, angular velocity, nonlocality parameter, wave number and gradient index have significant effect on the wave dispersion characteristics of the understudy nanobeam. The outcome of this study can provide beneficial information for the next generation researches and exact design of nano-machines including nanoscale molecular bearings and nanogears, etc.

키워드

참고문헌

  1. Ahouel, M., Houari, M.S.A., Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  2. Aranda-Ruiz, J., Loya, J. and Fernandez-Saez, J. (2012), "Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory", Compos. Struct., 94(9), 2990-3001. https://doi.org/10.1016/j.compstruct.2012.03.033
  3. Aydogdu, M. (2014), "Longitudinal wave propagation in multiwalled carbon nanotubes", Compos. Struct., 107, 578-584. https://doi.org/10.1016/j.compstruct.2013.08.031
  4. Ebrahimi, F. and Jafari, A. (2016), "Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory", Adv. Mater. Res., 5(4), 261-276.
  5. Ebrahimi, F., Ehyaei, J. and Babaei, R. (2016), "Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation", Adv. Mater. Res., 5(4), 245-261. https://doi.org/10.12989/amr.2016.5.4.245
  6. Ebrahimi, F. and Mohsen, D. (2016), "Dynamic modeling of embedded curved nanobeams incorporating surface effects", Coupled Syst. Mech., 5(3), 255-267. https://doi.org/10.12989/csm.2016.5.3.255
  7. 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(2), 151-181.
  8. 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
  9. Ebrahimi, F. and Salari, E. (2015), "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
  10. Ebrahimi, F. and Salari, E. (2015), "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
  11. Ebrahimi, F. and Salari, E. (2015), "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
  12. Ebrahimi, F. and Barati, M.R. (2016), "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
  13. Ebrahimi, F. and Barati, M.R. (2016), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2
  14. Ebrahimi, F. and Barati, M.R. (2016), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 42(5), 1715-1726.
  15. Ebrahimi, F. and Barati, M.R. (2016), "On nonlocal characteristics of curved inhomogeneous Euler-Bernoulli nanobeams under different temperature distributions", Appl. Phys. A, 122(10), 880. https://doi.org/10.1007/s00339-016-0399-7
  16. Ebrahimi, F. and Barati, M.R. (2016), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 24(11), 924-936.
  17. Ebrahimi, F. and Barati, M.R. (2016), "Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory", J. Therm. Stress., 39(12), 1560-1571. https://doi.org/10.1080/01495739.2016.1219243
  18. Ebrahimi, F. and Barati, M.R. (2016), "Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory", Appl. Phys. A, 122(9), 843. https://doi.org/10.1007/s00339-016-0368-1
  19. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vibr. Contr., 24(3), 549-564.
  20. Ebrahimi, F. and Barati, M.R. (2016h), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 39(3), 937-952.
  21. Ebrahimi, F. and Barati, M.R. (2016i), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., Just Accepted.
  22. Ebrahimi, F. and Barati, M.R. (2016j), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  23. Ebrahimi, F. and Barati, M.R. (2017a), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092
  24. Ebrahimi, F. and Barati, M.R. (2017b), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058
  25. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Double nanoplate-based NEMS under hydrostatic and electrostatic actuations", Eur. Phys. J. Plus, 131(5), 1-19. https://doi.org/10.1140/epjp/i2016-16001-3
  26. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates", Appl. Phys. A, 122(10), 922. https://doi.org/10.1007/s00339-016-0452-6
  27. Ebrahimi, F. and Hosseini, S.H.S. (2016c), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stress., 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  28. Ebrahimi, F. and Mokhtari, M. (2015), "Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method", J. Brazil. Soc. Mech. Sci. Eng., 37(4), 1435-1444. https://doi.org/10.1007/s40430-014-0255-7
  29. Ebrahimi, F. and Nasirzadeh, P. (2015), "A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method", J. Theoret. Appl. Mech., 53(4), 1041-1052.
  30. Ebrahimi, F. and Salari, E. (2015a), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007
  31. Ebrahimi, F. and Salari, E. (2015b), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronaut., 113, 29-50. https://doi.org/10.1016/j.actaastro.2015.03.031
  32. 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
  33. Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's 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
  34. Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronaut., 116, 117-125. https://doi.org/10.1016/j.actaastro.2015.06.014
  35. Ebrahimi, F., Barati, M.R. and Haghi, P. (2016), "Nonlocal thermo-elastic wave propagation in temperaturedependent embedded small-scaled nonhomogeneous beams", Eur. Phys. J. Plus, 131(11), 383. https://doi.org/10.1140/epjp/i2016-16383-0
  36. Ebrahimi, F., Barati, M.R. and Haghi, P. (2016), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Therm. Stress., 40(5), 535-547.
  37. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Therm. Stress., 40(5), 535-547. https://doi.org/10.1080/01495739.2016.1230483
  38. 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. Technol., 29(3), 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  39. 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. Technol., 29(3), 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  40. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016a), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccan., 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  41. 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. Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  42. 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. Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  43. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2016c), "In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams", Meccan., 51(4), 951-977. https://doi.org/10.1007/s11012-015-0248-3
  44. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded sizedependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  45. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5), 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026
  46. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X
  47. 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
  48. Farajpour, A., Yazdi, M.H., Rastgoo, A. and Mohammadi, M. (2016), "A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment", Acta Mech., 227(7), 1849-1867. https://doi.org/10.1007/s00707-016-1605-6
  49. Filiz, S. and Aydogdu, M. (2015), "Wave propagation analysis of embedded (coupled) functionally graded nanotubes conveying fluid", Compos. Struct., 132, 1260-1273. https://doi.org/10.1016/j.compstruct.2015.07.043
  50. Fotouhi, M.M., Firouz-Abadi, R.D. and Haddadpour, H. (2013), "Free vibration analysis of nanocones embedded in an elastic medium using a nonlocal continuum shell model", Int. J. Eng. Sci., 64, 14-22. https://doi.org/10.1016/j.ijengsci.2012.12.003
  51. Lam, D.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Sol., 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  52. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013
  53. Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 133, 1079-1092. https://doi.org/10.1016/j.compstruct.2015.08.014
  54. Li, L., Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010
  55. Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91. https://doi.org/10.1016/j.ijengsci.2017.11.021
  56. Lim, C.W. and Yang, Y. (2010), "Wave propagation in carbon nanotubes: Nonlocal elasticity-induced stiffness and velocity enhancement effects", J. Mech. Mater. Struct., 5(3), 459-476. https://doi.org/10.2140/jomms.2010.5.459
  57. Mohammadi, M., Safarabadi, M., Rastgoo, A. and Farajpour, A. (2016), "Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment", Acta Mech., 227(8), 2207-2232. https://doi.org/10.1007/s00707-016-1623-4
  58. Narendar, S. (2016), "Wave dispersion in functionally graded magneto-electro-elastic nonlocal rod", Aerosp. Sci. Technol., 51, 42-51. https://doi.org/10.1016/j.ast.2016.01.012
  59. Narendar, S. and Gopalakrishnan, S. (2009), "Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes", Comput. Mater. Sci., 47(2), 526-538. https://doi.org/10.1016/j.commatsci.2009.09.021
  60. Narendar, S. and Gopalakrishnan, S. (2011), "Axial wave propagation in coupled nanorod system with nonlocal small scale effects", Compos. Part B: Eng., 42(7), 2013-2023. https://doi.org/10.1016/j.compositesb.2011.05.021
  61. Narendar, S. and Gopalakrishnan, S. (2011), "Nonlocal wave propagation in rotating nanotube", Res. Phys., 1(1), 17-25. https://doi.org/10.1016/j.rinp.2011.06.002
  62. Narendar, S., Gupta, S.S. and Gopalakrishnan, S. (2012), "Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 36(9), 4529-4538. https://doi.org/10.1016/j.apm.2011.11.073
  63. Pradhan, K.K. and Chakraverty, S. (2013), "Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method", Compos. Part B: Eng., 51, 175-184. https://doi.org/10.1016/j.compositesb.2013.02.027
  64. Pradhan, S.C. and Murmu, T. (2010), "Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever", Phys. E: Low-Dimens. Syst. Nanostruct., 42(7), 1944-1949. https://doi.org/10.1016/j.physe.2010.03.004
  65. Srivastava, D. (1997), "A phenomenological model of the rotation dynamics of carbon nanotube gears with laser electric fields", Nanotechnol., 8(4), 186. https://doi.org/10.1088/0957-4484/8/4/005
  66. Wang, L. (2010), "Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory", Comput. Mater. Sci., 49(4), 761-766. https://doi.org/10.1016/j.commatsci.2010.06.019
  67. Yang, F.A.C.M., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Sol. Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  68. Yang, Y., Zhang, L. and Lim, C.W. (2011), "Wave propagation in double-walled carbon nanotubes on a novel analytically nonlocal Timoshenko-beam model", J. Sound Vibr., 330(8), 1704-1717. https://doi.org/10.1016/j.jsv.2010.10.028
  69. Zhang, D.G. (2013), "Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory", Compos. Struct., 100, 121-126. https://doi.org/10.1016/j.compstruct.2012.12.024
  70. Zhang, S., Liu, W.K. and Ruoff, R.S. (2004), "Atomistic simulations of double-walled carbon nanotubes (DWCNTs) as rotational bearings", Nano Lett., 4(2), 293-297. https://doi.org/10.1021/nl0350276
  71. Zhu, X. and Li, L. (2017a), "Twisting statics of functionally graded nanotubes using Eringen's nonlocal integral model", Compos. Struct., 178, 87-96. https://doi.org/10.1016/j.compstruct.2017.06.067
  72. Zhu, X. and Li, L. (2017b), "On longitudinal dynamics of nanorods", Int. J. Eng. Sci., 120, 129-145. https://doi.org/10.1016/j.ijengsci.2017.08.003
  73. Zhu, X. and Li, L. (2017c), "Closed form solution for a nonlocal strain gradient rod in tension", Int. J. Eng. Sci., 119, 16-28. https://doi.org/10.1016/j.ijengsci.2017.06.019