DOI QR코드

DOI QR Code

On nonlinear vibration behavior of piezo-magnetic doubly-curved nanoshells

  • Mirjavadi, Sayed Sajad (Department of Mechanical and Industrial Engineering, Qatar University) ;
  • Bayani, Hassan (Department of Electrical Engineering, Instituto Superior Tecnico) ;
  • Khoshtinat, Navid (Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University) ;
  • Forsat, Masoud (Department of Mechanical and Industrial Engineering, Qatar University) ;
  • Barati, Mohammad Reza (Fidar Project Qaem Company) ;
  • Hamouda, A.M.S (Department of Mechanical and Industrial Engineering, Qatar University)
  • Received : 2020.01.17
  • Accepted : 2020.07.31
  • Published : 2020.11.25

Abstract

In this paper, nonlinear vibration behaviors of multi-phase Magneto-Electro-Elastic (MEE) doubly-curved nanoshells have been studied employing Jacobi elliptic function method. The doubly-curved nanoshell has been modeled by using nonlocal elasticity and classic shell theory. An exact estimation of nonlinear vibrational behavior of smart doubly-curved nanoshell has been obtained via Jacobi elliptic function method. This method can incorporate the influences of higher order harmonics leading to an exact estimation of nonlinear vibration frequency. It will be indicated that nonlinear vibrational frequency of doubly-curved nanoshell relies on nonlocal effect, material composition, curvature radius, center deflection and electro-magnetic field.

Keywords

Acknowledgement

The authors would like to thank FPQ (Fidar project Qaem) for providing the fruitful and useful help.

References

  1. Aboudi, J. (2001), "Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites", Smart Mater. Struct., 10(5), 867. https://doi.org/10.1088/0964-1726/10/5/303.
  2. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., Int. J., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  3. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., Int. J., 18(6), 1125-1143. http://dx.doi.org/10.12989/sss.2016.18.6.1125.
  4. Al-Maliki, A.F., Faleh, N.M. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Struct. Monit. Maint., Int. J., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147.
  5. Alasadi, A.A., Ahmed, R.A. and Faleh, N.M. (2019), "Analyzing nonlinear vibrations of metal foam nanobeams with symmetric and non-symmetric porosities", Adv. Aircr. Spacecr. Sci., Int. J., 6(4), 273-282. https://doi.org/10.12989/aas.2019.6.4.273.
  6. Annigeri, A.R., Ganesan, N. and Swarnamani, S. (2007), "Free vibration behaviour of multiphase and layered magneto-electroelastic beam", J. Sound Vib., 299(1-2), 44-63. https://doi.org/10.1016/j.jsv.2006.06.044.
  7. Azimi, M., Mirjavadi, S.S., Shafiei, N. and Hamouda, A.M.S. (2017), "Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam", Appl. Phys. A, 123(1), 104. https://doi.org/10.1007/s00339-016-0712-5.
  8. Barati, M.R. (2017), "Coupled effects of electrical polarizationstrain gradient on vibration behavior of double-layered flexoelectric nanoplates", Smart Struct. Syst., Int. J., 20(5), 573-581. https://doi.org/10.12989/sss.2017.20.5.573.
  9. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., Int. J., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115.
  10. 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.
  11. 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.
  12. Eshraghi, I., Jalali, S.K. and Pugno, N.M. (2016), "Imperfection sensitivity of nonlinear vibration of curved single-walled carbon nanotubes based on nonlocal timoshenko beam theory", Materials, 9(9), 786. https://doi.org/10.3390/ma9090786.
  13. Fenjan, R.M., Ahmed, R.A., Alasadi, A.A. and Faleh, N.M. (2019), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and nonuniform porosities", Coupled Syst. Mech., Int. J., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247.
  14. Guo, J., Chen, J. and Pan, E. (2016), "Static deformation of anisotropic layered magnetoelectroelastic plates based on modified couple-stress theory", Compos. Part B Eng., 107, 84-96. https://doi.org/10.1016/j.compositesb.2016.09.044.
  15. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells", Smart Mater. Struct., 23(12), 125036. https://doi.org/10.1088/0964-1726/23/12/125036.
  16. Kumaravel, A., Ganesan, N. and Sethuraman, R. (2007), "Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment", Multidiscip. Model. Mater. Struct., 3(4), 461-476. https://doi.org/10.1163/157361107782106401.
  17. Li, Y. and Shi, Z. (2009), "Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature", Compos. Struct., 87(3), 257-264. https://doi.org/10.1016/j.compstruct.2008.01.012.
  18. Liu, S., Fu, Z., Liu, S. and Zhao, Q. (2001), "Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations", Phys. Lett. A, 289(1-2), 69-74. https://doi.org/10.1016/S0375-9601(01)00580-1.
  19. Liu, H., Liu, H. and Yang, J. (2018), "Vibration of FG magnetoelectro-viscoelastic porous nanobeams on visco-Pasternak foundation", Compos. Part B Eng., 155, 244-256. https://doi.org/10.1016/j.compositesb.2018.08.042.
  20. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1929. https://doi.org/10.1177%2F1099636217727577. https://doi.org/10.1177/1099636217727577
  21. Marinca, V. and Herişanu, N. (2011), "Explicit and exact solutions to cubic Duffing and double-well Duffing equations", Math. Comput. Model., 53(5-6), 604-609. https://doi.org/10.1016/j.mcm.2010.09.011.
  22. Mirjavadi, S.S., Matin, A., Shafiei, N., Rabby, S. and Mohasel Afshari, B. (2017a), "Thermal buckling behavior of twodimensional imperfect functionally graded microscale-tapered porous beam", J. Therm. Stress., 40(10), 1201-1214. https://doi.org/10.1080/01495739.2017.1332962.
  23. Mirjavadi, S.S., Rabby, S., Shafiei, N., Afshari, B.M. and Kazemi, M. (2017b), "On size-dependent free vibration and thermal buckling of axially functionally graded nanobeams in thermal environment", Appl. Phys. A, 123(5), 315. https://doi.org/10.1007/s00339-017-0918-1.
  24. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2018a), "Strain gradient based dynamic response analysis of heterogeneous cylindrical microshells with porosities under a moving load", Mater. Res. Express, 6(3), 035029. https://doi.org/10.1088/2053-1591/aaf5a2.
  25. Mirjavadi, S.S., Afshari, B.M., Khezel, M., Shafiei, N., Rabby, S. and Kordnejad, M. (2018b), "Nonlinear vibration and buckling of functionally graded porous nanoscaled beams", J. Braz. Soc. Mech. Sci. Eng., 40(7), 352. https://doi.org/10.1007/s40430-018-1272-8.
  26. Mirjavadi, S.S., Mohasel Afshari, B., Shafiei, N., Rabby, S. and Kazemi, M. (2018c), "Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam", J. Vib. Control, 24(18), 4211-4225. https://doi.org/10.1177%2F1077546317721871. https://doi.org/10.1177/1077546317721871
  27. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2019a), "Nonlinear free and forced vibrations of graphene nanoplatelet reinforced microbeams with geometrical imperfection", Microsyst. Technol., 25(8), 3137-3150. https://doi.org/10.1007/s00542-018-4277-4.
  28. Mirjavadi, S.S., Afshari, B.M., Barati, M.R. and Hamouda, A.M.S. (2019b), "Transient response of porous inhomogeneous nanobeams due to various impulsive loads based on nonlocal strain gradient elasticity", Int. J. Mech. Mater. Des., 2019, 1-12. https://doi.org/10.1007/s10999-019-09452-2.
  29. Mirjavadi, S.S., Forsat, M., Nikookar, M., Barati, M.R. and Hamouda, A.M.S. (2019c), "Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets", Eur. Phys. J. Plus, 134(10), 508. https://doi.org/10.1140/epjp/i2019-12806-8.
  30. Mirjavadi, S.S., Forsat, M., Badnava, S., Barati, M.R. and Hamouda, A.M.S. (2020), "Nonlinear dynamic characteristics of nonlocal multi-phase magneto-electro-elastic nano-tubes with different piezoelectric constituents", Appl. Phys. A, 126(8), 1-16. https://doi.org/10.1007/s00339-020-03743-8.
  31. Mohammadi, H., Mahzoon, M., Mohammadi, M. and Mohammadi, M. (2014), "Postbuckling instability of nonlinear nanobeam with geometric imperfection embedded in elastic foundation", Nonlin. Dyn., 76(4), 2005-2016. https://doi.org/10.1007/s11071-014-1264-x.
  32. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., Int. J., 59(3), 431-454. http://dx.doi.org/10.12989/sem.2016.59.3.431.
  33. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., Int. J., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.
  34. Mouffoki, A., Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., Int. J., 20(3), 369-383. https://doi.org/10.12989/sss.2017.19.2.115.
  35. Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3-4), 321-339. https://doi.org/10.1016/j.ijengsci.2004.09.006.
  36. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063.
  37. 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.
  38. Wang, H., Chen, L., Liu, H. and Zheng, S. (2016), "Nonlinear dynamics and exact traveling wave solutions of the higher-order nonlinear Schrödinger equation with derivative non-kerr nonlinear terms", Math. Probl. Eng., 2016, 7405141. https://doi.org/10.1155/2016/7405141.
  39. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., Int. J., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015.
  40. Zhang, S., Zhao, S. and Xu, B. (2020), "Analytical insights into a generalized semidiscrete system with time-varying coefficients: Derivation, exact solutions and nonlinear soliton dynamics", Complexity, 2020, 1543503. https://doi.org/10.1155/2020/1543503.

Cited by

  1. Analyzing dynamic response of nonlocal strain gradient porous beams under moving load and thermal environment vol.26, pp.1, 2020, https://doi.org/10.12989/gae.2021.26.1.089
  2. Finite element simulation for investigation on thermal post-buckling of geometrically imperfect GOP-reinforced beam vol.12, pp.2, 2021, https://doi.org/10.12989/acc.2021.12.2.135
  3. Nonlinear vibration behavior of hybrid multi-scale cylindrical panels via semi numerical method vol.28, pp.3, 2021, https://doi.org/10.12989/cac.2021.28.3.233
  4. Numerical forced vibration analysis of compositionally gradient porous cylindrical microshells under moving load and thermal environment vol.40, pp.6, 2021, https://doi.org/10.12989/scs.2021.40.6.893