Advances in nano research

  • 제6권4호
  • /
  • Pages.399-422
  • /
  • 2018
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Vibration analysis thermally affected viscoelastic nanosensors subjected to linear varying loads

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Babaei, Ramin (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Shaghaghi, Gholam Reza (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2018.08.23
  • 심사 : 2018.11.22
  • 발행 : 2018.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

Unwanted vibration is an issue in many industrial systems, especially in nano-devices. There are many ways to compensate these unwanted vibrations based on the results of the past researches. Elastic medium and smart material etc. are effective methods to restrain unnecessary vibration. In this manuscript, dynamic analysis of viscoelastic nanosensor which is made of functionally graded (FGM) nanobeams is investigated. It is assumed that, the shaft is flexible. The system is modeled based on Timoshenko beam theory and also environmental condition, external linear varying loads and thermal loading effect are considered. The equations of motion are extracted by using energy method and Hamilton principle to describe the translational and shear deformation's behavior of the system. Governing equations of motion are extracted by supplementing Eringen's nonlocal theory. Finally vibration behavior of system especially the frequency of system is developed by implementation Semi-analytical differential transformed method (DTM). The results are validated in the researches that have been done in the past and shows good agreement with them.

키워드

참고문헌

  1. Ansari, R., Oskouie, M.F. and Gholami, R. (2016), "Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory", Phys. E: Lowdimens. Syst. Nanostruct., 75, 266-271.
  2. Arda, M. and Aydogdu, M. (2017), Longitudinal Vibration of CNTs Viscously Damped in Span.
  3. Barooti, M.M., Safarpour, H. and Ghadiri, M. (2017), "Critical speed and free vibration analysis of spinning 3D single-walled carbon nanotubes resting on elastic foundations", Eur. Phys. J. Plus, 132(1), 6.
  4. Chen, S.S. (2004), "Application of the differential transformation method to a non-linear conservative system", Appl. Math. Computat., 154(2), 431-441. https://doi.org/10.1016/S0096-3003(03)00723-9
  5. Duan, K., Li, Y., Li, L., Hu, Y. and Wang, X. (2018), "Diamond nanothread based resonators: ultrahigh sensitivity and low dissipation", Nanoscale, 10(17), 8058-8065.
  6. Ebrahimi, F. and Barati, M.R. (2016a), "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.
  7. Ebrahimi, F. and Barati, M.R. (2016b), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 1077546316646239.
  8. Ebrahimi, F. and Barati, M.R. (2016c), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910.
  9. Ebrahimi, F. and Barati, M.R. (2016d), "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
  10. Ebrahimi, F. and Barati, M.R. (2016e), "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. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  12. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y
  13. Ebrahimi, F. and Barati, M.R. (2016h), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  14. Ebrahimi, F. and Barati, M.R. (2016i), "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
  15. Ebrahimi, F. and Barati, M.R. (2016j), "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
  16. Ebrahimi, F. and Barati, M.R. (2017), "A third-order parabolic shear deformation beam theory for nonlocal vibration analysis of magneto-electro-elastic nanobeams embedded in two-parameter elastic foundation", Adv. Nano Res., Int. J., 5(4), 313-336. https://doi.org/10.21474/IJAR01/4719
  17. 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/10.21474/IJAR01/7340
  18. Ebrahimi, F. and Dabbagh, A. (2016), "On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory", Compos. Struct., 162, 281-293.
  19. Ebrahimi, F. and Farazmandnia, N. (2017), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mech. Adv. Mater. Struct., 24(10), 820-829.
  20. Ebrahimi, F. and Habibi, S. (2017), "Low-velocity impact response of laminated FG-CNT reinforced composite plates in thermal environment", Adv. Nano Res., Int. J., 5(2), 69-97.
  21. Ebrahimi, F. and Haghi, P. (2018), "Wave dispersion analysis of rotating heterogeneous nanobeams in thermal environment", Adv. Nano Res., Int. J., 6(1), 21-37.
  22. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "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
  23. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "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
  24. Ebrahimi, F. and Mahmoodi, F. (2018), "Vibration analysis of carbon nanotubes with multiple cracks in thermal environment", Adv. Nano Res., Int. J., 6(1), 57-80.
  25. Ebrahimi, F. and Shaghaghi, G.R. (2015), "Vibration analysis of an initially pre-stressed rotating carbon nanotube employing differential transform method", Int. J. Adv. Des. Manuf. Technol., 8(4), 13-21.
  26. Ebrahimi, F. and Shaghaghi, G.R. (2016), "Thermal effects on nonlocal vibrational characteristics of nanobeams with non-ideal boundary conditions", Smart Struct. Syst., Int. J., 18(6), 1087-1109.
  27. Ebrahimi, F. and Shaghaghi, G.R. (2018), "Nonlinear vibration analysis of electro-hygro-thermally actuated embedded nanobeams with various boundary conditions", Microsyst. Technol., 24(12), 5037-5054.
  28. Ebrahimi, F., Shaghaghi, G.R. and Salari, E. (2014), "Vibration analysis of size-dependent nano beams basedon nonlocal timoshenko beam theory", J. Mech. Eng. Technol. (JMET), 6(2).
  29. Ebrahimi, F., Boreiry, M. and Shaghaghi, G. (2015), "Investigating the surface elasticity and tension effects on critical buckling behaviour of nanotubes based on differential transformation method", J. Mech. Eng. Technol. (JMET), 7(1).
  30. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016a), "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
  31. Ebrahimi, F., Shaghaghi, G.R. and Boreiry, M. (2016b), "A semi-analytical evaluation of surface and nonlocal effects on buckling and vibrational characteristics of nanotubes with various boundary conditions", Int. J. Struct. Stabil. Dyn., 16(6), 1550023.
  32. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2016c), "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
  33. Ebrahimi, F., Ehyaei, J. and Babaei, R. (2016d), "Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation", Adv. Mater. Res., Int. J., 5(4), 245-261.
  34. Ebrahimi, F., Babaei, R. and Shaghaghi, G.R. (2018), "Nonlocal buckling characteristics of heterogeneous plates subjected to various loadings", Adv. Aircr. Spacecr. Sci., 5(5), 515-531. https://doi.org/10.12989/aas.2018.5.5.515
  35. Ehyaei, J., Ebrahimi, F. and Salari, E. (2016), "Nonlocal vibration analysis of FG nano beams with different boundary conditions", Adv. Nano Res., Int. J., 4(2), 85-111.
  36. 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.
  37. Elishakoff, I., Challamel, N., Soret, C., Bekel, Y. and Gomez, T. (2013), "Virus sensor based on single-walled carbon nanotube: improved theory incorporating surface effects", Phil. Trans. R. Soc. A, 371(1993), 20120424. https://doi.org/10.1098/rsta.2012.0424
  38. Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Computat., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072
  39. 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
  40. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  41. Fernandes, R., El-Borgi, S., Mousavi, S.M., Reddy, J.N. and Mechmoum, A. (2017), "Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium", Physica E: Low-dimens. Syst. Nanostruct., 88, 18-25. https://doi.org/10.1016/j.physe.2016.11.007
  42. Ghadiri, M., Ebrahimi, F., Salari, E., Hosseini, S.A.H. and Shaghaghi, G.R. (2015), "Electro-thermo-mechanical vibration analysis of embedded single-walled boron nitride nanotubes based on nonlocal third-order beam theory", Int. J. Multiscale Computat. Eng., 13(5).
  43. Hassan, I.A.H. (2002), "On solving some eigenvalue problems by using a differential transformation", Appl. Math. Comput., 127(1), 1-22. https://doi.org/10.1016/S0096-3003(00)00123-5
  44. Hwang, H.J., Jung, S.L., Cho, K.H., Kim, Y. and Jang, H. (2010), "Tribological performance of brake friction materials containing carbon nanotubes", Wear, 268(3-4), 519-525. https://doi.org/10.1016/j.wear.2009.09.003
  45. Ju, S.P. (2004), "Application of differential transformation to transient advective-dispersive transport equation", Appl. Math. Comput., 155(1), 25-38. https://doi.org/10.1016/S0096-3003(03)00755-0
  46. Karlicic, D., Kozic, P., Adhikari, S., Cajic, M., Murmu, T. and Lazarevic, M. (2015), "Nonlocal mass-nanosensor model based on the damped vibration of single-layer graphene sheet influenced by in-plane magnetic field", Int. J. Mech. Sci., 96, 132-142.
  47. Li, L. and Hu, Y. (2017), "Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects", Int. J. Mech. Sci., 120, 159-170. https://doi.org/10.1016/j.ijmecsci.2016.11.025
  48. Li, X.F., Tang, G.J., Shen, Z.B. and Lee, K.Y. (2015), "Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory", Ultrasonics, 55, 75-84. https://doi.org/10.1016/j.ultras.2014.08.002
  49. Marzbanrad, J., Ebrahimi-Nejad, S., Shaghaghi, G. and Boreiry, M. (2018b), "Nonlinear vibration analysis of piezoelectric functionally graded nanobeam exposed to combined hygro-magneto-electro-thermo-mechanical loading", Mater. Res. Express, 5(7), 075022. https://doi.org/10.1088/2053-1591/aad0ce
  50. Miller, R.E. and Shenoy, V.B. (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnology, 11(3), 139. https://doi.org/10.1088/0957-4484/11/3/301
  51. Mohammadimehr, M., Mohammadi-Dehabadi, A.A. and Maraghi, Z.K. (2017), "The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow", Phys. B: Condensed Matter, 510, 48-59.
  52. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta metallurgica, 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  53. Murmu, T. and Adhikari, S. (2013), "Nonlocal mass nanosensors based on vibrating monolayer graphene sheets", Sensors Actuators B: Chem., 188, 1319-1327.
  54. Pradhan, S.C. and Phadikar, J.K. (2011), "Nonlocal theory for buckling of nanoplates", Int. J. Struct. Stabil. Dyn., 11(3), 411-429. https://doi.org/10.1142/S021945541100418X
  55. Wang, Z.G. (2013), "Axial vibration analysis of stepped bar by differential transformation method", In: Applied Mechanics and Materials (Vol. 419, pp. 273-279), Trans Tech Publications.
  56. Wu, H.L., Yang, J. and Kitipornchai, S. (2016), "Nonlinear vibration of functionally graded carbon nanotube-reinforced composite beams with geometric imperfections", Compos. Part B: Eng., 90, 86-96.
  57. Zhou, C.W., Sun, X.K., Laine, J.P., Ichchou, M.N., Zine, A., Hans, S. and Boutin, C. (2018), "Wave Propagation Feature in Two-Dimensional Periodic Beam Lattices with Local Resonance by Numerical Method and Analytical Homogenization Approach", Int. J. Appl. Mech., 1850042.
  58. Zhu, X. and Li, L. (2017), "On longitudinal dynamics of nanorods", Int. J. Eng. Sci., 120, 129-145.