ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

On the Fuzzy Sliding Mode Control of Nonlinear Motions in a Laminated Beam

Journal of Applied Nonlinear Dynamics 1(3) (2012) 287--307 | DOI:10.5890/JAND.2012.07.004

L. Dai$^{1}$,$^{2}$; L. Sun$^{2}$

$^{1}$ Civil and Architecture Engineering, Xiamen University of Technology, China

$^{2}$ Industrial Systems Engineering, University of Regina, Canada

Download Full Text PDF

Abstract

A modified fuzzy sliding mode control (MFSMC) strategy is devel-oped in this research for actively controlling and stabilizing the non-linear vibration of a laminated composite cantilever beam. The cantilever beam model, which is wildly seen in engineering applications, is established based on Hamilton’s principle through the application of Reddy’s third-order theory together with von Karman-type equations. Geometric nonlinearity of the beam is considered.The governing equations for the beam are derived corresponding to the higher order discretization of Galerkin method. By the model developed with n degrees of freedom, a vibration control strategy is developed on the basis of the modification of the fuzzy sliding mode control (FSMC). The vibration control strategy of the present research provides the availability for controlling the vibrations of such beam in n degrees of freedom. The approach is also proven to be effective in stabilizing the vibration of the nonlinear beam in a desired manner.

References

1.  [1] Pai, P.F., and Nayfeh, A.H. (1990), Nonlinear non-planar oscillation of a cantilever beam under lateral base excitations, International Journal of Non-linear Mechanics, 25 (5), 455-474.
2.  [2] Dwivedy, S.K., and Kar, R. C. (2003), Nonlinear dynamics of a cantilever beam carrying an attached mass with 1:3:9 internal resonances, Nonlinear Dynamics, 31 (1), 49-72.
3.  [3] Alsaleem, F.M., Younis, H. L., and Quakad, H. M. (2009), On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators, Journal of Micromechanics and Microengineering, 19 (4), 1-14.
4.  [4] Mergen, M.H., and Paidoussis, M. P. (2010), Three-dimensional dynamics of a cantilever pipe conveying fluid, additionally supported by anintermediate spring array, International Journal of Non-Linear Mechanics, 45 (5), 507-524.
5.  [5] Karmar, V., Miller, J.K., and Rhoads, J. F. (2011), Nonlinear parametric amplification and attenuation in a based excited cantilever beam, Journal of Sound and Vibration, 330 (22), 5401-5409.
6.  [6] Utkin, V.I. (1992), Sliding modes in control and optimization, Springer-Verlag, Berlin, 1992.
7.  [7] Yau, H.T., Kuo, C.L. (2006), Fuzzy sliding mode control for a class of chaos synchronization with uncertainties, International Journal of Nonlinear Sciences and Numerical Simulation, 7 (3), 333-338.
8.  [8] Kuo, C.L., Shieh, C.S., Lin. C.H., and Shih, S.P. (2007), Design of fuzzy sliding-mode controller for chaos synchronization, Communication in Computer and Information Science, 5, 36-45.
9.  [9] Yau, H.T.,Wang, C.C., Hsieh, C.T., and Cho, C.C. (2011), Nonlinear analysis and control of the uncertain micro-electromechanical system by using a fuzzy sliding mode control design, Computers and Mathematics with Applications, 61 (8), 1912-1916.
10.  [10] Haghighi, H.H., and Markazi, A. H. D. (2010), Chaos prediction and control in MEMS resonators, Communications in Nonlinear Science and Numerical Simulation, 15 (10), 3091-3099.
11.  [11] Nosier, A., Reddy, J.N. (1991), A study of non-linear dynamic equations of higher-order deformation plate theories. International Journal of Non-Linear Mechanics, 26 (2), 233-249.
12.  [12] Abou-Rayan, A.M., A.H. Nayfeh, D. T. Mook, and A. M. Nayfeh (1993), Nonlinear response of a parametrically excited bucked beam, Nonlinear Dynamics, 4, 499-525.
13.  [13] Yao, Z., Zhang, W., and Chen, L. (2009), Bifurcation, chaotic dynamics and control of piezoelectric laminated composite beam, Chinese Journal of Theoretical and Applied Mechanics, 41, 129-140.
14.  [14] Dai, L. (2008), Nonlinear dynamics of piece constant systems and implementation of piecewise constant arguments, World Scientific, New Jersey.