Advances in nano research

  • 제5권4호
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  • Pages.313-336
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  • 2017
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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

A third-order parabolic shear deformation beam theory for nonlocal vibration analysis of magneto-electro-elastic nanobeams embedded in two-parameter elastic foundation

  • Ebrahimi, Farzad (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University) ;
  • Barati, Mohammad Reza (Aerospace Engineering Department & Center of Excellence in Computational Aerospace, Amirkabir University of Technology)
  • 투고 : 2016.11.15
  • 심사 : 2017.05.04
  • 발행 : 2017.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

This article investigates vibration behavior of magneto-electro-elastic functionally graded (MEE-FG) nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of MEE-FG nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen's nonlocal elasticity theory which captures the small size effects and using the Hamilton's principle, the nonlocal governing equations of motions are derived and then solved analytically. Then the influences of elastic foundation, magnetic potential, external electric voltage, nonlocal parameter, power-law index and slenderness ratio on the frequencies of the embedded MEE-FG nanobeams are studied.

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참고문헌

  1. Annigeri, A.R., Ganesan, N. and Swarnamani, S. (2007), "Free vibration behaviour of multiphase and layered magneto-electro-elastic beam", J. Sound Vib., 299(1), 44-63. https://doi.org/10.1016/j.jsv.2006.06.044
  2. Ansari, R., Hasrati, E., Gholami, R. and Sadeghi, F. (2015), "Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto-electro-thermo elastic nanobeams", Compos. Part B: Eng.
  3. Kumaravel, A., Ganesan, N. and Sethuraman, R. (2007), "Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment", Multidiscipl. Model. Mater. Struct., 3(4), 461-476. https://doi.org/10.1163/157361107782106401
  4. Daga, A., Ganesan, N. and Shankar, K. (2009), "Transient dynamic response of cantilever magneto-electro-elastic beam using finite elements", Int. J. Computat. Methods Eng. Sci. Mech., 10(3), 173-185. https://doi.org/10.1080/15502280902797207
  5. Ebrahimi, F. (2013), "Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment", Mech. Adv. Mater. Struct., 20(10), 854-870. https://doi.org/10.1080/15376494.2012.677098
  6. Ebrahimi, F. and Barati, M.R. (2015), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 40, 1-12. https://doi.org/10.1007/s13369-014-1492-x
  7. Ebrahimi, F. and Barati, M.R. (2016a), "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
  8. Ebrahimi, F. and Barati, M.R. (2016b), "An exact solution for buckling analysis of embedded piezoelectromagnetically actuated nanoscale beams", Adv. Nano Res., Int. J., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  9. Ebrahimi, F. and Barati, M.R. (2016c), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 1-16.
  10. Ebrahimi, F. and Barati, M.R. (2016d), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intel. Mater. Syst. Struct., 1045389X16672569.
  11. Ebrahimi, F. and Barati, M.R. (2016e), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  12. Ebrahimi, F. and Barati, M.R. (2016f), "Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment", Int. J. Smart Nano Mater., 1-22.
  13. Ebrahimi, F. and Barati, M.R. (2016g), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 1-12.
  14. Ebrahimi, F. and Barati, M.R. (2016h), "Magnetic field effects on buckling behavior of smart sizedependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  15. Ebrahimi, F. and Barati, M.R. (2016i), "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. (2016j), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9
  17. Ebrahimi, F. and Barati, M.R. (2016k), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 24(11), 924-936.
  18. Ebrahimi, F. and Barati, M.R. (2016l), "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
  19. Ebrahimi, F. and Barati, M.R. (2016m), "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.
  20. Ebrahimi, F. and Barati, M.R. (2016n), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 1077546316646239.
  21. Ebrahimi, F. and Barati, M.R. (2016o), "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
  22. Ebrahimi, F. and Dabbagh, A. (2016), "On flexural wave propagation responses of smart FG magnetoelectro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct.
  23. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., Int. J., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  24. 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
  25. 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
  26. 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
  27. Ebrahimi, F. and Barati, M.R. (2017a), "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
  28. Ebrahimi, F. and Barati, M.R. (2017b), "Buckling analysis of smart size-dependent higher order magnetoelectro-thermo-elastic functionally graded nanosize beams", J. Mech., 33(1), 23-33. https://doi.org/10.1017/jmech.2016.46
  29. Ebrahimi, F. and Barati, M.R. (2017c), "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
  30. Ebrahimi, F. and Mokhtari, M. (2014), "Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method", J. Brazil. Soc. Mech. Sci. Eng., 1-10.
  31. Ebrahimi, F. and Rastgoo, A. (2009), "Nonlinear vibration of smart circular functionally graded plates coupled with piezoelectric layers", Int. J. Mech. Mater. Des., 5(2), 157-165. https://doi.org/10.1007/s10999-008-9091-1
  32. Ebrahimi, F. and Rastgoo, A. (2011), "Nonlinear vibration analysis of piezo-thermo-electrically actuated functionally graded circular plates", Archive Appl. Mech., 81(3), 361-383. https://doi.org/10.1007/s00419-010-0415-x
  33. 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
  34. Ebrahimi, F. and Salari, E. (2015a-b), "Thermo-mechanical vibration analysis of nonlocal temperaturedependent FG nanobeams with various boundary conditions", Compos. Part B: Eng., 78, 272-290. https://doi.org/10.1016/j.compositesb.2015.03.068
  35. Ebrahimi, F. and Salari, E. (2015b-c), "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
  36. Ebrahimi, F. and Salari, E. (2016), "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
  37. 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
  38. Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Technol., 23(8), 2107-2124. https://doi.org/10.1007/s12206-009-0358-8
  39. 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. Thermal Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  40. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016a), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  41. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2016b), "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
  42. 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
  43. Huang, D.J., Ding, H.J. and Chen, W.Q. (2007), "Analytical solution for functionally graded magnetoelectro-elastic plane beams", Int. J. Eng. Sci., 45(2), 467-485. https://doi.org/10.1016/j.ijengsci.2007.03.005
  44. Kattimani, S.C. and Ray, M.C. (2015), "Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates", Int. J. Mech. Sci.
  45. Ke, L.L. and Wang, Y.S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory", Physica E: Low-Dimens. Syst. Nanostruct., 63, 52-61. https://doi.org/10.1016/j.physe.2014.05.002
  46. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "Free vibration of size-dependent magnetoelectro-elastic nanoplates based on the nonlocal theory", Acta Mechanica Sinica, 30(4), 516-525. https://doi.org/10.1007/s10409-014-0072-3
  47. Li, X.Y., Ding, H.J. and Chen, W.Q. (2008), "Three-dimensional analytical solution for functionally graded magneto-electro-elastic circular plates subjected to uniform load", Compos. Struct., 83(4), 381-390. https://doi.org/10.1016/j.compstruct.2007.05.006
  48. Li, Y.S., Cai, Z.Y. and Shi, S.Y. (2014), "Buckling and free vibration of magnetoelectroelastic nanoplate based on nonlocal theory", Compos. Struct., 111, 522-529. https://doi.org/10.1016/j.compstruct.2014.01.033
  49. Milazzo, A., Orlando, C. and Alaimo, A. (2009), "An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem", Smart Mater. Struc., 18(8), 085012. https://doi.org/10.1088/0964-1726/18/8/085012
  50. 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
  51. Razavi, S. and Shooshtari, A. (2015), "Nonlinear free vibration of magneto-electro-elastic rectangular plates", Compos. Struct., 119, 377-384. https://doi.org/10.1016/j.compstruct.2014.08.034
  52. Shooshtari, A. and Razavi, S. (2015), "Large amplitude free vibration of symmetrically laminated magnetoelectro-elastic rectangular plates on Pasternak type foundation", Mech. Res. Commun., 69, 103-113. https://doi.org/10.1016/j.mechrescom.2015.06.011
  53. 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
  54. 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
  55. Wang, Y., Chen, W. and Li, X. (2015), "Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam", Appl. Math. Mech., 36(5), 581-598. https://doi.org/10.1007/s10483-015-1934-7
  56. 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
  57. Wu, B., Zhang, C., Chen, W. and Zhang, C. (2015), "Surface effects on anti-plane shear waves propagating in magneto-electro-elastic nanoplates", Smart Mater. Struct., 24(9), 095017. https://doi.org/10.1088/0964-1726/24/9/095017

피인용 문헌

  1. Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method vol.10, pp.1, 2017, https://doi.org/10.12989/anr.2021.10.1.025