Vibration Control of a Functionally Graded Carbon Nanotube-Reinforced Composites Beam Resting on Elastic Foundation

Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati

Abstract:

In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.

Keywords: Carbon nanotubes, vibration control, piezoelectric layers, elastic foundation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125843

References:

[1] A.M.K. Esawi, M.M. Farag, “Carbon nanotube reinforced composites: potential and current challenges”, Mater Des, vol.28, pp.2394–401, 2007.
[2] Y. Han, J. Elliott, “Molecular dynamics simulations of the elastic properties of Polymer/carbon nanotube composites”, Compute Mater Sci, vol.39, pp.315–23, 2007.
[3] H.S. Shen, “Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments”, Compos Struct, vol.91, pp.9–19, 2009.
[4] Ke L-L, Yang J, Kitipornchai S, “Nonlinear free vibration of functionally graded carbon nanotube-reinforced composit beams”, Compos Struct, vol.92, pp.676–83, 2010.
[5] M. Rafiee, J. Yang, S. Kitipornchai, “Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers”, Composite Structures, vol.96, pp.716-725, 2013.
[6] M.H. Yas, N. Samadi, ”Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation”, Int J Pres Ves Pip, vol.98, pp.119–28, 2012.
[7] A. Mahieddine and M. Ouali, “Finite element formulation of a beam with piezoelectric patch”, J. Eng. Appl. Sci, vol.3, pp.803–807, 2008.
[8] S. Li, H. Su and C. Cheng, “Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment”, Appl. Math. Mech., Vol.30, pp.969–982, 2009.
[9] H. Shen and Y. Xiang, “Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments”, Engineering Structures, vol.56, pp.698–708, 2013.
[10] H. Shen and Y. Xiang,” Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments”, Composite Structures, vol.111, pp.291–300, 2013.
[11] R. Ansari, M. FaghihShojaei, V. Mohammadi, R. Gholami, F. Sadeghi, “Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams”, Compos Struct, vol.113, pp.316-327, 2014.
[12] V. Azadi, M. Azadi, S.A. Fazelzadeh, E. Azadi, “Active control of a FGM beam under follower force with piezoelectric sensors/actuators, IJSSD, vol.3, 1350063 (19 pages), 2014.
[13] K. Yildirim, I. Kucuk, “Active piezoelectric vibration control for a Timoshenko beam”, Journal of the Franklin Institute, vol.353, pp.95-107, 2016.