Structural Engineering and Mechanics

  • 제66권2호
  • /
  • Pages.237-248
  • /
  • 2018
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Wave propagation analysis of smart strain gradient piezo-magneto-elastic nonlocal beams

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Barati, Mohammad Reza (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2017.12.22
  • 심사 : 2018.02.03
  • 발행 : 2018.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

This study presents the investigation of wave dispersion characteristics of a magneto-electro-elastic functionally graded (MEE-FG) nanosize beam utilizing nonlocal strain gradient theory (NSGT). In this theory, a material length scale parameter is propounded to show the influence of strain gradient stress field, and likewise, a nonlocal parameter is nominated to emphasize on the importance of elastic stress field effects. The material properties of heterogeneous nanobeam are supposed to vary smoothly through the thickness direction based on power-law form. Applying Hamilton's principle, the nonlocal governing equations of MEE-FG nanobeam are derived. Furthermore, to derive the wave frequency, phase velocity and escape frequency of MEE-FG nanobeam, an analytical solution is employed. The validation procedure is performed by comparing the results of present model with results exhibited by previous papers. Results are rendered in the framework of an exact parametric study by changing various parameters such as wave number, nonlocal parameter, length scale parameter, gradient index, magnetic potential and electric voltage to show their influence on the wave frequency, phase velocity and escape frequency of MEE-FG nanobeams.

키워드

참고문헌

  1. Akgoz, B. and Civalek, O. (2016), "Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory", Acta Astronaut., 119, 1-12. https://doi.org/10.1016/j.actaastro.2015.10.021
  2. Ansari, R., Gholami, R. and Rouhi, H. (2015), "Size-dependent nonlinear forced vibration analysis of magneto-electro-thermoelastic Timoshenko nanobeams based upon the nonlocal elasticity theory", Compos. Struct., 126, 216-226. https://doi.org/10.1016/j.compstruct.2015.02.068
  3. Arani, A.G., Jamali, M., Ghorbanpour-Arani, A.H., Kolahchi, R. and Mosayyebi, M. (2016), "Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects", Proceedings of the Institution of Mechanical Engineers.
  4. Arefi, M. (2016), "Analysis of wave in a functionally graded magneto-electro-elastic nano-rod using nonlocal elasticity model subjected to electric and magnetic potentials", Acta Mech., 1-14.
  5. Barati, M.R., Shahverdi, H. and Zenkour, A.M. (2016), "Electromechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory", Mech. Adv. Mater. Struct., Just Accepted.
  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. Civalek, O . And Demir, C . (2016), "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Math. Comput., 289, 335-352.
  8. Ebrahimi, F. and Barati, M.R. (2016a), "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
  9. Ebrahimi, F. and Barati, M.R. (2016d), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  10. Ebrahimi, F. and Barati, M.R. (2016e), "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
  11. Ebrahimi, F. and Barati, M.R. (2016a), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vibr. Contr., 1077546316646239.
  12. Ebrahimi, F. and Barati, M.R. (2016b), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., Just Accepted.
  13. Ebrahimi, F. and Barati, M.R. (2016c), "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. (2016f), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  15. Ebrahimi, F. and Boreiry, M. (2015), "Investigating various surface effects on nonlocal vibrational behavior of nanobeams", Appl. Phys. A, 121(3), 1305-1316. https://doi.org/10.1007/s00339-015-9512-6
  16. 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.
  17. 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
  18. Ebrahimi, F. and Shafiei, N. (2016), "Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory", Mech. Adv. Mater. Struct., Just Accepted.
  19. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  20. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015b), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and nonlinear temperature distributions", J. Therm. Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  21. 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
  22. 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
  23. 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
  24. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-35. https://doi.org/10.1016/0020-7225(72)90050-X
  25. 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., 1-19.
  26. Fu, Y., Du, H. and Zhang, S. (2003), "Functionally graded TiN/TiNi shape memory alloy films", Mater. Lett., 57(20), 2995-2999. https://doi.org/10.1016/S0167-577X(02)01419-2
  27. Ghadiri, M., Shafiei, N. and Safarpour, H. (2016), "Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen's nonlocal elasticity", Microsyst. Technol., 1-21.
  28. Hasanyan, D.J., Batra, R.C. and Harutyunyan, S. (2008), "Pull-in instabilities in functionally graded microthermoelectromechanical systems", J. Therm. Stress., 31(10), 1006-1021. https://doi.org/10.1080/01495730802250714
  29. 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
  30. 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
  31. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory", Acta Mech. Sin., 30(4), 516-525. https://doi.org/10.1007/s10409-014-0072-3
  32. Li, C., Lim, C.W. and Yu, J.L. (2010), "Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axial load", Smart Mater. Struct., 20(1), 015023. https://doi.org/10.1088/0964-1726/20/1/015023
  33. 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
  34. Li, L. and Hu, Y. (2016b), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011
  35. 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
  36. Li, L., Li, X. and Hu, Y. (2016a), "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
  37. Li, X.Y., Ding, H.J. and Chen, W.Q. (2008), "Three-dimensional analytical solution for functionally graded magneto-electroelastic circular plates subjected to uniform load", Compos. Struct., 83(4), 381-390. https://doi.org/10.1016/j.compstruct.2007.05.006
  38. Lim, C.W., Li, C. and Yu, J.L. (2009), "The effects of stiffness strengthening nonlocal stress and axial tension on free vibration of cantilever nanobeams", Interact. Multisc. Mech., 2(3), 223-233. https://doi.org/10.12989/imm.2009.2.3.223
  39. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Sol., 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  40. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory", Int. J. Sol. Struct., 46(5), 1176-1185. https://doi.org/10.1016/j.ijsolstr.2008.10.012
  41. 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
  42. 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
  43. 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
  44. Rahaeifard, M., Kahrobaiyan, M.H. and Ahmadian, M.T. (2009), "Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials", Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers.
  45. Ramirez, F., Heyliger, P.R. and Pan, E. (2006), "Discrete layer solution to free vibrations of functionally graded magnetoelectro-elastic plates", Mech. Adv. Mater. Struct., 13(3), 249-266. https://doi.org/10.1080/15376490600582750
  46. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45(2), 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  47. Simsek, M. (2014), "Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory", Compos. Part B: Eng., 56, 621-628. https://doi.org/10.1016/j.compositesb.2013.08.082
  48. 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
  49. Thai, H.T. and Vo, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009
  50. Wang, Y., Li, F. and Kishimoto, K. (2010), "Scale effects on flexural wave propagation in nanoplate embedded in elastic matrix with initial stress", Appl. Phys. A, 99, 907-911. https://doi.org/10.1007/s00339-010-5666-4
  51. Witvrouw, A. and Mehta, A. (2005), The Use of Functionally Graded Poly-SiGe Layers for MEMS Applications, Trans Tech Publications.
  52. Zang, J., Fang, B., Zhang, Y.W., Yang, T.Z. and Li, D.H. (2014), "Longitudinal wave propagation in a piezoelectric nanoplate considering surface effects and nonlocal elasticity theory", Phys. E: Low-Dimens. Syst. Nanostruct., 63, 147-150. https://doi.org/10.1016/j.physe.2014.05.019
  53. Zhang, L.L., Liu, X.J. and Nie, G.Q. (2014b), "Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates", Eur. J. Mech., 46, 22-29. https://doi.org/10.1016/j.euromechsol.2014.01.005
  54. Zhang, Y.W., Chen, J., Zeng, W., Teng, Y.Y., Fang, B. and Zang, J. (2015), "Surface and thermal effects of the flexural wave propagation of piezoelectric functionally graded nanobeam using nonlocal elasticity", Comput. Mater. Sci., 97, 222-226. https://doi.org/10.1016/j.commatsci.2014.10.046

피인용 문헌

  1. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2018, https://doi.org/10.12989/sem.2019.70.4.407
  2. Nonlinear vibration and stability of FG nanotubes conveying fluid via nonlocal strain gradient theory vol.78, pp.1, 2021, https://doi.org/10.12989/sem.2021.78.1.103