DOI QR코드

DOI QR Code

Vibration analysis of functionally graded nanocomposite plate moving in two directions

  • Arani, Ali Ghorbanpour (Faculty of Mechanical Engineering, Institute of Nanoscience & Nanotechnology, University of Kashan) ;
  • Haghparast, Elham (Faculty of Mechanical Engineering, Institute of Nanoscience & Nanotechnology, University of Kashan) ;
  • Zarei, Hassan BabaAkbar (Faculty of Mechanical Engineering, Institute of Nanoscience & Nanotechnology, University of Kashan)
  • Received : 2016.10.17
  • Accepted : 2017.01.26
  • Published : 2017.04.10

Abstract

In the present study, vibration analysis of functionally graded carbon nanotube reinforced composite (FGCNTRC) plate moving in two directions is investigated. Various types of shear deformation theories are utilized to obtain more accurate and simplest theory. Single-walled carbon nanotubes (SWCNTs) are selected as a reinforcement of composite face sheets inside Poly methyl methacrylate (PMMA) matrix. Moreover, different kinds of distributions of CNTs are considered. Based on extended rule of mixture, the structural properties of composite face sheets are considered. Motion equations are obtained by Hamilton's principle and solved analytically. Influences of various parameters such as moving speed in x and y directions, volume fraction and distribution of CNTs, orthotropic viscoelastic surrounding medium, thickness and aspect ratio of composite plate on the vibration characteristics of moving system are discussed in details. The results indicated that thenatural frequency or stability of FGCNTRC plate is strongly dependent on axially moving speed. Moreover, a better configuration of the nanotube embedded in plate can be used to increase the critical speed, as a result, the stability is improved. The results of this investigation can be used in design and manufacturing of marine vessels and aircrafts.

Keywords

vibration${\backslash}$vibration analysis;plate;fiber reinforced polymers (FRP);sandwich composite;composite structures

Acknowledgement

Supported by : University of Kashan

References

  1. An, C. and Su, J. (2014), "Dynamic analysis of axially moving orthotropic plates: Integral transforms solution", Appl. Math. Comput., 228, 489-507.
  2. Banichuk, N., Jeronen, J., Neittaanmaki, P. and Tuovinen, T. (2010), "On the instability of an axially moving elastic plate", Int. J. Solids Struct., 47(1), 91-99. https://doi.org/10.1016/j.ijsolstr.2009.09.020
  3. Banichuk, N., Jeronen, J., Kurki, M., Neittaanmaki, P., Saksa, T. and Tuovinen, T. (2011), "On the limit velocity and buckling phenomena of axially moving orthotropic membranes and plates", Int. J. Solids Struct., 48(13), 2015-2025. https://doi.org/10.1016/j.ijsolstr.2011.03.010
  4. Ghayesh, M.H., Amabili, M. and Païdoussis, M.P. (2013), "Nonlinear dynamics of axially moving plates", J. Sound Vib., 332(2), 391-406. https://doi.org/10.1016/j.jsv.2012.08.013
  5. Ghorbanpour Arani, A. and Haghparast, E. (2016), "Sizedependent vibration of axially moving viscoelastic microplates based on sinusoidal shear deformation theory", Int. J. Appl. Mech.
  6. Ghorbanpour Arani, A., Haghparast, E. and Baba Akbar Zarei, H. (2016), "Vibration of axially moving 3-phase CNTFPC plate resting on orthotropic foundation", Struct. Eng. Mech., Int. J., 57(1), 105-126. https://doi.org/10.12989/sem.2016.57.1.105
  7. Gibson, R.F. (1994), Principles of Composite Material Mechanics, McGraw-Hill, Inc, New York, USA.
  8. Hatami, S., Azhari, M. and Saadatpour, M.M. (2007), "Free vibration of moving laminated composite plates", Compos. Struct., 80(4), 609-620. https://doi.org/10.1016/j.compstruct.2006.07.009
  9. Hatami, S., Ronagh, H.R. and Azhari, M. (2008), "Exact free vibration analysis of axially moving viscoelastic plates", Comput. Struct., 86(17), 1738-1746. https://doi.org/10.1016/j.compstruc.2008.02.002
  10. Kim, J., Cho, J., Lee, U. and Park, S. (2003), "Modal spectral element formulation for axially moving plates subjected to inplane axial tension", Comput. Struct., 81(20), 2011-2020. https://doi.org/10.1016/S0045-7949(03)00229-3
  11. Lin, C.C. (1997), "Stability and vibration characteristics of axially moving plates", Int. J. Solids Struct., 34(24), 3179-3190. https://doi.org/10.1016/S0020-7683(96)00181-3
  12. Marynowski, K. (2010), "Free vibration analysis of the axially moving Levy-type viscoelastic plate", Eur. J. Mech. A Solids, 29(5), 879-886. https://doi.org/10.1016/j.euromechsol.2010.03.010
  13. Marynowski, K. and Grabski, J. (2013), "Dynamic analysis of an axially moving plate subjected to thermal loading", Mech. Res. Commun., 51, 67-71. https://doi.org/10.1016/j.mechrescom.2013.05.004
  14. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077
  15. Tang, Y.Q. and Chen, L.Q. (2011), "Nonlinear free transverse vibrations of in-plane moving plates: Without and with internal resonances", J. Sound Vib., 330(1), 110-126. https://doi.org/10.1016/j.jsv.2010.07.005
  16. Tang, Y.Q. and Chen, L.Q. (2012), "Primary resonance in forced vibrations of in-plane translating viscoelastic plates with 3:1 internal resonance", Nonlinear Dyn., 69(1), 159-172. https://doi.org/10.1007/s11071-011-0253-6
  17. Wang, X. (1999), "Numerical analysis of moving orthotropic thin plates", Comput. Struct., 70(4), 467-486. https://doi.org/10.1016/S0045-7949(98)00161-8
  18. Wang, Z.X. and Shen, H.S. (2012), "Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets", Composites Part B, 43(2), 411-421. https://doi.org/10.1016/j.compositesb.2011.04.040
  19. Wang, C.M., Reddy, J.N. and Lee, K.H. (2000), Shear Deformable Beams and Plates, Elsevier.
  20. Yang, T. and Fang, B. (2013), "Asymptotic analysis of an axially viscoelastic string constituted by a fractional differentiation law", Int. J. Non-Linear Mech., 49, 170-174. https://doi.org/10.1016/j.ijnonlinmec.2012.10.001
  21. Yang, T., Fang, B., Chen, Y. and Zhen, Y. (2009), "Approximate solutions of axially moving viscoelastic beams subject to multifrequency excitations", Int. J. Non-Linear Mech., 44(2), 230-238 https://doi.org/10.1016/j.ijnonlinmec.2008.11.013
  22. Yang, X.D., Chen, L.Q. and Zu, J.W. (2011), "Vibrations and stability of an axially moving rectangular composite plate", J. Appl. Mech., 78(1), 11018-11028. https://doi.org/10.1115/1.4002002
  23. Yang, X.D., Zhang, W., Chen, L.Q. and Yao, M.H. (2012), "Dynamical analysis of axially moving plate by finite difference method", Nonlinear Dyn., 67(2), 997-1006. https://doi.org/10.1007/s11071-011-0042-2
  24. Yang, T., Fang, B., Yang, X.D. and Li, Y. (2013), "Closed-form approximate solution for natural frequency of axially moving beams", Int. J. Mech. Sci., 74, 154-160. https://doi.org/10.1016/j.ijmecsci.2013.05.010
  25. Zho, Y. and Wang, Z. (2008), "Vibrations of axially moving viscoelastic plate with parabolically varying thickness", J. Sound Vib., 316(1), 198-210. https://doi.org/10.1016/j.jsv.2008.02.040
  26. Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced compo-site plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010

Cited by

  1. Nonlinear free and forced vibration analysis of FG-CNTRC annular sector plates pp.02728397, 2018, https://doi.org/10.1002/pc.24998
  2. Vibration analysis of functionally graded rectangular plates partially resting on elastic supports using the first-order shear deformation theory and differential quadrature element method vol.41, pp.2, 2019, https://doi.org/10.1007/s40430-019-1600-7