DOI QR코드

DOI QR Code

Surface effect on forced vibration of DNS by viscoelastic layer under a moving load

  • Hosseini, S.A.H. (Buin Zahra Higher Education Center of Engineering and Technology, Imam Khomeini International University) ;
  • Rahmani, O. (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan) ;
  • Hayati, H. (Faculty of Engineering and Information Technology, University of Technology Sydney) ;
  • Jahanshir, A. (Buin Zahra Higher Education Center of Engineering and Technology, Imam Khomeini International University)
  • Received : 2020.10.18
  • Accepted : 2021.07.01
  • Published : 2021.08.25

Abstract

The surface effect for a forced vibration of a double-nanobeam-system (DNS) coupled by a viscoelastic layer under a moving constant load is studied in this paper. The viscoelastic layer that couples the nanobeams to each other, is modelled as spring-damper system. The Euler- Bernoulli theory and a simply supported boundary condition are considered for both nanobeams. By using the analytical solution, the dynamic displacement is obtained by considering the surface elasticity and residual tension effect on each nanobeams. Furthermore, the several significant parameters such as the velocity of the moving load, spring constant, damping coefficient and also the surface effect have been studied using some plots and examples. Finally, by observing the diagrams it was concluded that as the length of the beams reduces, the surface effect has a considerable effect on each of nanobeams especially at Nano scale, where it was not achieved by classic theories.

Keywords

References

  1. Akgoz, B. and Civalek, O . (2015), "A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory", Acta Mechanica, 226(7), 2277-2294. https://doi.org/10.1007/s00707-015-1308-4.
  2. Akgoz, B. and Civalek, O . (2017), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng., 129 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024.
  3. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  4. Alizadeh Hamidi, B., Khosravi, F., Hosseini, S.A. and Hassannejad, R. (2020), "Free torsional vibration of triangle microwire based on modified couple stress theory", J. Strain Anal. Eng. Des., 55(7-8), 237-245. https://doi.org/10.1177/0309324720922385.
  5. Arda, M. and Aydogdu, M. (2017), "Longitudinal vibration of CNTs viscously damped in span", Int. J. Eng. Appl. Sci., 9(2), 22-38. https://doi.org/10.24107/ijeas.305348.
  6. Aydogdu, M. and Arda, M. (2016), "Forced vibration of nanorods using nonlocal elasticity", Adv. Nano Res., 4(4), 265. http://doi.org/10.12989/anr.2016.4.4.265.
  7. Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., 6(3), 257. http://doi.org/10.12989/anr.2018.6.3.257.
  8. Bastanfar, M., Hosseini, S.A., Sourki, R. and Khosravi, F. (2019), "Flexoelectric and surface effects on a cracked piezoelectric nanobeam: Analytical resonant frequency response", Arch. Mech. Eng., 66(4), 417-437. http://doi.org/10.24425/ame.2019.131355.
  9. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  10. Choudhary, N. and Kaur, D. (2015), "Vibration damping materials and their applications in nano/microelectro-mechanical systems: a review", J. Nanosci. Nanotechnol., 15(3), 1907-1924. https://doi.org/10.1166/jnn.2015.10324.
  11. Darvishvand, A. and Zajkani, A. (2019), "Size-dependent plastic buckling behavior of micro-beam structures by using conventional mechanism-based strain gradient plasticity", Struct. Eng. Mech., 71(3), 223-232. https://doi.org/10.12989/sem.2019.71.3.223.
  12. Demir, C. and Civalek, O. (2017), "On the analysis of microbeams", Int. J. Eng. Sci., 121 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016.
  13. Dingreville, R., Qu, J. and Cherkaoui, M. (2005). "Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films", J. Mech. Phys. Solid., 53(8), 1827-1854. https://doi.org/10.1016/j.jmps.2005.02.012.
  14. Eichenfield, M., Chan, J., Camacho, R.M., Vahala, K.J. and Painter, O. (2009), "Optomechanical crystals", Nature., 462(7269), 78-82. https://doi.org/10.1038/nature08524.
  15. El-Borgi, S., Fernandes, R. and Reddy, J.N. (2015), "Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation", Int. J. Nonlin. Mech., 77 348-363. https://doi.org/10.1016/j.ijnonlinmec.2015.09.013.
  16. Fedorov, A.S., Novikov, P., Martinez, Y.S. and Churilov, G. (2007), "Influence of buffer gas and vibration temperature of carbon clusters on fullerene formation in a carbon plasma", J. Nanosci. Nanotechnol., 7(4-5), 1315-1320. https://doi.org/10.1166/jnn.2007.309.
  17. 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.
  18. Gao, Y., Xiao, W. and Zhu, H. (2019), "Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method", Struct. Eng. Mech., 69 205-219. http://doi.org/10.12989/sem.2019.69.2.205.
  19. Ghadiri, M., Hosseini, S.A.H., Karami, M. and Namvar, M. (2018), "In-plane and out of plane free vibration of U-shaped AFM probes based on the nonlocal elasticity", J. Solid Mech., 10(2), 285-299.
  20. Gurtin, M., Weissmuller, J. and Larche, F.J.P.M.A. (1998), "A general theory of curved deformable interfaces in solids at equilibrium", Philos. Mag. A, 78(5), 1093-1109. https://doi.org/10.1080/01418619808239977.
  21. Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089.
  22. Hamidi, B.A., Hosseini, S.A. and Hayati, H. (2020), "Forced torsional vibration of nanobeam via nonlocal strain gradient theory and surface energy effects under moving harmonic torque", Wave. Rand. Complex Media, 1-16. https://doi.org/10.1080/17455030.2020.1772523.
  23. Hassannejad, R., Hosseini, S.A. and Alizadeh-Hamidi, B. (2020), "Influence of non-circular cross section shapes on torsional vibration of a micro-rod based on modified couple stress theory", Acta Astronautica, 178 805-812. https://doi.org/10.1016/j.actaastro.2020.10.005.
  24. Hosseini, S. and Rahmani, O. (2016), "Surface effects on buckling of double nanobeam system based on nonlocal Timoshenko model", Int. J. Struct. Stab. Dyn., 16(10), 1550077. https://doi.org/10.1142/S0219455415500777.
  25. Hosseini, S.A., Khosravi, F. and Ghadiri, M. (2019), "Moving axial load on dynamic response of single-walled carbon nanotubes using classical, Rayleigh and Bishop rod models based on Eringen's theory", J. Vib. Control., 1077546319890170. https://doi.org/10.1177/1077546319890170.
  26. Khosravi, F., Hosseini, S.A. and Hayati, H. (2020), "Free and forced axial vibration of single walled carbon nanotube under linear and harmonic concentrated forces based on nonlocal theory", Int. J. Modern Phys. B, 2050067. https://doi.org/10.1142/S0217979220500678.
  27. Kim, P. and Lieber, C.M. (1999), "Nanotube nanotweezers", Sci., 286(5447), 2148-2150. https://doi.org/10.1126/science.286.5447.214.
  28. Kunbar, L.A.H., Alkadhimi, B.M., Radhi, H.S. and Faleh, N.M. (2020), "Flexoelectric effects on dynamic response characteristics of nonlocal piezoelectric material beam", Adv. Mater. Res., 8(4), 259. : https://doi.org/10.12989/amr.2019.8.4.259.
  29. Liang, L.N., Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2015), "Flexural vibration of an atomic force microscope cantilever based on modified couple stress theory", Int. J. Struct. Stab. Dyn., 15(07), 1540025. https://doi.org/10.1142/S0219455415400258.
  30. Liew, K.M., He, X. and Kitipornchai, S. (2006), "Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix", Acta Materialia, 54(16), 4229-4236. https://doi.org/10.1016/j.actamat.2006.05.016.
  31. Miller, R.E. and Shenoy, V.B.J.N. (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnol., 11(3), 139. https://doi.org/10.1088/0957-4484/11/3/301
  32. Murmu, T. and Adhikari, S. (2010), "Nonlocal transverse vibration of double-nanobeam-systems", J. Appl. Phys., 108(8), 083514. https://doi.org/10.1063/1.3496627.
  33. Murmu, T. and Adhikari, S. (2011), "Nonlocal vibration of bonded double-nanoplate-systems", Compos. Part B: Eng., 42(7), 1901-1911. https://doi.org/10.1016/j.compositesb.2011.06.009.
  34. Norouzzadeh, A., Ansari, R. and Rouhi, H. (2020), "An analytical study on wave propagation in functionally graded nano-beams/tubes based on the integral formulation of nonlocal elasticity", Wave. Rand. Complex Media, 30(3), 562-580. https://doi.org/10.1080/17455030.2018.1543979.
  35. O zgur Yayli, M. (2016), "An efficient solution method for the longitudinal vibration of nanorods with arbitrary boundary conditions via a hardening nonlocal approach", J. Vib. Control., 24(11), 2230-2246. https://doi.org/10.1177/1077546316684042.
  36. Pirmohammadi, A., Pourseifi, M., Rahmani, O. and Hoseini, S. (2014), "Modeling and active vibration suppression of a single-walled carbon nanotube subjected to a moving harmonic load based on a nonlocal elasticity theory", Appl. Phys. A, 117(3), 1547-1555. https://doi.org/10.1007/s00339-014-8592-z.
  37. Pouresmaeeli, S., Fazelzadeh, S. and Ghavanloo, E. (2012), "Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium", Compos. Part B: Eng., 43(8), 3384-3390. https://doi.org/10.1016/j.compositesb.2012.01.046.
  38. Pourseifi, M., Rahmani, O. and Hoseini, S.A.H. (2015), "Active vibration control of nanotube struct ures under a moving nanoparticle based on the nonlocal continuum theories", Meccanica, 50(5), 1 351-1369. https://doi.org/10.1007/s11012-014-0096-6.
  39. Radic, N., Jeremic, D., Trifkovic, S. and Milutinovic, M. (2014), "Buckling analysis of double-orthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory", Compos. Part B: Eng., 61 162-171. https://doi.org/10.1016/j.compositesb.2014.01.042.
  40. Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A. and Chemi, A. (2016), "Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory", Adv. Nano Res., 4(1), 31. http://doi.org/10.12989/anr.2016.4.1.031.
  41. Reddy, J.N., Romanoff, J. and Loya, J.A. (2016), "Nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory", Eur. J. Mech.-A/Solid., 56 92-104. https://doi.org/10.1016/j.euromechsol.2015.11.001.
  42. Sharma, P., Ganti, S. and Bhate, N. (2003), "Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities", Appl. Phys. Lett., 82(4), 535-537. https://doi.org/10.1063/1.1539929.
  43. Vu, H., Ordonez, A. and Karnopp, B. (2000), "Vibration of a double-beam system", J. Sound Vib., 229(4), 807-822. https://doi.org/10.1006/jsvi.1999.2528.
  44. Wang, G.F. and Feng, X.Q. (2007), "Effects of surface elasticity and residual surface tension on the natural frequency of microbeams", Appl. Phys. Lett., 90(23), 231904. https://doi.org/10.1063/1.2746950.
  45. Yayli, M.O. (2018), "On the torsional vibrations of restrained nanotubes embedded in an elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 40(9), 419. https://doi.org/10.1007/s40430-018-1346-7.
  46. Yayli, M.O. (2015), "Stability analysis of gradient elastic microbeams with arbitrary boundary conditions", J. Mech. Sci. Technol., 29(8), 3373-3380. https://doi.org/10.1007/s12206-015-0735-4.