Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear forced vibration of sandwich plate with considering FG core and CNTs reinforced nano-composite face sheets

  • Rostami, Rasoul (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Rahaghi, Mohsen Irani (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2019.04.13
  • Accepted : 2020.07.21
  • Published : 2020.08.25
⟨ Previous Next ⟩

Abstract

Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

Keywords

Acknowledgement

The research described in this paper was financially supported by the Natural Science Foundation.

References

  1. Alijani, F. and Amabili, M. (2013), "Nonlinear vibrations of laminated and sandwich rectangular plates with free edges. Part 1: Theory and numerical simulations", Compos. Struct., 105, 422-436. https://doi.org/10.1016/j.compstruct.2013.05.034
  2. Asnafi, A. and Abedi, M.A. (2015), "A complete analogical study on the dynamic stability analysis of isotropic functionally graded plates subjected to lateral stochastic loads", Acta Mech., 226(7), 2347-2363. https://doi.org/10.1007/s00707-015-1321-7
  3. Chaudhari, V.K., Gupta, A. and Talha, M. (2016), "Nonlinear Vibration response of shear deformable functionally graded plate using finite element method", Proceedings of the 3rd International Conference on Innovations in Automation and Mechatronics Engineering. https://doi.org/10.1016/j.protcy.2016.03.018
  4. Chi, S.H. and Chung, Y.L. (2006), "Mechanical behavior of functionally graded material plates under transverse load-Part I: analysis", Int. J. Solids Struct., 43, 3657-3674. https://doi.org/10.1016/j.compstruct.2013.05.034
  5. Chien, R.D. and Chen, C.S. (2005), "Nonlinear vibration of laminated plates on a nonlinear elastic foundation", Compos. Struct., 70, 90-99. https://doi.org/10.1016/j.compstruct.2004.08.015
  6. Chien, R.D. and Chen, C.S. (2006), "Nonlinear vibration of laminated plates on an elastic foundation", Thin-Wall. Struct., 44, 852-860. https://doi.org/10.1016/j.tws.2006.08.016
  7. Darabi, M. and Ganesan, R. (2017), "Nonlinear dynamic instability analysis of laminated composite thin plates subjected to periodic in-plane loads", Nonlinear Dyn., 91, 187-215. https://doi.org/10.1007/s11071-017-3863-9
  8. Duc, N.D., Cong, P.H. and Quang, V.D. (2016), "Nonlinear dynamic and vibration analysis of piezoelectric eccentrically stiffened FGM plates in thermal environment", Int. J. Mech. Sci., 115, 711-722. https://doi.org/10.1007/s11071-017-3863-9
  9. Fan, Y., Xiang, Y., Shen, H.S. and Hui, D. (2018), "Nonlinear lowvelocity impact response of FG-GRC laminated plates resting on viscoelastic foundations", Compos. Part B: Eng., 144, 184-194. https://doi.org/10.1016/j.compositesb.2018.02.016
  10. Gholamia, R. and Ansari R. (2018), "Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates", Eng. Struct., 156, 197-209. https://doi.org/10.1016/j.engstruct.2017.11.019
  11. Han, W. and Petyt, M. (1997), "Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method-I: The fundamental mode of isotropic plates", Comput. Struct., 63(2), 295-308. https://doi.org/10.1016/S0045-7949(96)00345-8
  12. Houmat, A. (2013), "Nonlinear free vibration of laminated composite rectangular plates with curvilinear fibers", Compos. Struct., 106, 211-224. https://doi.org/10.1016/j.compstruct.2013.05.058
  13. Kattimani, S.C. and Ray, M.C. (2014), "Smart damping of geometrically nonlinear vibrations of magneto-electro-elastic plates", Compos. Struct., 114, 51-63. https://doi.org/10.1016/j.compstruct.2014.03.050
  14. Liu, Y. and Chu, F. (2012), "Nonlinear vibrations of rotating thin circular cylindrical shell", Nonlinear Dyn., 67, 1467-1479. https://doi.org/10.1007/s11071-011-0082-7
  15. Mohammadimehr, M. and Rostami, R. (2018), "Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields", Appl. Mathe. Mech., 39(2), 219-240. https://doi.org/10.1007/s10483-018-2301-6
  16. Mohammadimehr, M., Rostami R. and Arefi, M. (2016a), "Electroelastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., Int. J., 20(3), 513-544. https://doi.org/10.12989/scs.2016.20.3.513
  17. Mohammadimehr, M., Rousta Navia, B. and Ghorbanpour Arani, A. (2016b), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of doublecoupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Struct. part B: Eng., 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007
  18. Nematollahi, M.S. and Mohammadi, H. (2019), "Geometrically nonlinear vibration analysis of sandwich nanoplates based on higher-order nonlocal strain gradient theory", Int. J. Mech. Sci., 156, 31-45. https://doi.org/10.1016/j.ijmecsci.2019.03.022
  19. Razavi, S. and Shooshtari, A. (2014), "Nonlinear free vibration of magneto-electro-elastic rectangular plates", Compos. Struct., 119, 377-384. https://doi.org/10.1016/j.compstruct.2014.08.034
  20. Shahverdi, H. and Khalafi, V. (2016), "Bifurcation analysis of FG curved panels under simultaneous aerodynamic and thermal loads in hypersonic flow", Compos. Struct., 146, 84-94. https://doi.org/10.1016/j.compstruct.2016.03.011
  21. Shen, H.S. and Xiang, Y. (2014), "Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments", Compos. Struct., 111, 291-300. https://doi.org/10.1016/j.compstruct.2014.01.010
  22. Singha, M.K. and Daripa, R. (2009), "Nonlinear vibration and dynamic stability analysis of composite plates", J. Sound Vib., 328, 541-554. https://doi.org/10.1016/j.jsv.2009.08.020
  23. Solanki, M.K., Mishra, S.K., Shukla, K.K. and Singh, J. (2015), "Nonlinear free vibration of laminated composite and sandwich plates using multiquadric collocations", Proceedings of the 4th International Conference on Materials Processing and Characterization. https://doi.org/10.1016/j.matpr.2015.07.210
  24. Soni, S., Jain, N.K. and Joshi, P.V. (2017), "Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid", Nonlinear Dyn., 90,137-170. https://doi.org/10.1007/s11071-017-3652-5
  25. Talha, M. and Singh, B.N. (2011), "Thermo-mechanical induced vibration characteristics of shear deformable functionally graded ceramic-metal plates using finite element method", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225(1), 50-65. https://doi.org/10.1243/09544062JMES2115
  26. Teng, M.W. and Wang, Y.Q. (2020), "Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: Approximate analytical solution", Results in Physics, 17. https://doi.org/10.1016/j.rinp.2020.103147.
  27. Torabi, J. and Ansari, R. (2017), "Nonlinear free vibration analysis of thermally induced FG-CNTRC annular plates: Asymmetric versus axisymmetric study", Comput. Methods Appl. Mech. Eng., 324, 327-347. https://doi.org/10.1016/j.cma.2017.05.025
  28. Xue, C.X., Pan, E., Han, Q.K., Zhang, S.Y. and Chu, H.J. (2011), "Non-linear principal resonance of an orthotropic and magnetoelastic rectangular plate", Int. J. Non-Linear Mech., 46, 703-710. https://doi.org/10.1016/j.ijnonlinmec.2011.02.002
  29. Yang, J., Huang, X.H. and Shen, S.H. (2020), "Nonlinear vibration of temperature-dependent FG-CNTRC laminated plates with negative Poisson's ratio", Thin Wall. Struct., 148. https://doi.org/10.1016/j.tws.2019.106514
  30. Zeng, S. Wang, B.L. and Wang, K.F. (2019), "Nonlinear vibration of piezoelectric sandwich nanoplates with functionally graded porous core with consideration of flexoelectric effect", Compos. Struct., 207, 340-351. https://doi.org/10.1016/j.compstruct.2018.09.040

Cited by

  1. Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method vol.27, pp.1, 2020, https://doi.org/10.12989/cac.2021.27.1.073
  2. Free Vibration Analysis of Cylindrical Micro/Nano-Shell Reinforced with CNTRC Patches vol.13, pp.4, 2020, https://doi.org/10.1142/s175882512150040x