Vibration Suppression of Simply Supported Beam under a Moving Mass using On-Line Neural Network Controller

Document Type: Research Paper

Authors

1 University of Applied Science and Technology, Center of Mammut, Tehran, Iran

2 Faculty of Engineering, The University of Imam Ali, Tehran, Iran

Abstract

In this paper, model reference neural network structure is used as a controller for vibration suppression of the Euler–Bernoulli beam under the excitation of moving mass travelling along a vibrating path. The non-dimensional equation of motion the beam acted upon by a moving mass is achieved.  A Dirac-delta function is used to describe the position of the moving mass along the beam and its inertial effects.  Analytical solution the equation of motion is presented for simply supported boundary condition. The hybrid controller of system includes of a controller network and an identifier network. The neural networks are multilayer feed forward and trained simultaneously. The performance and robustness of the proposed controller are evaluated for various values mass ratio of the moving mass to the beam and dimensionless velocity of a moving mass on the time history of deflection. The simulations verify effectiveness and robustness of controller.                

Keywords


[1] Kononov A.V., De Borst R., 2002, Instability analysis of vibrations of a uniformly moving mass in one and two-dimensional elastic systems, European Journal of Mechanics-A/Solids 21(1): 151-165.
[2] Frýba L., 2013, Vibration of Solids and Structures under Moving Loads, Springer Science & Business Media.
[3] Bilello C., Lawrence A.B., Daniel K., 2004, Experimental investigation of a small-scale bridge model under a moving mass, Journal of Structural Engineering 130(5): 799-804.
[4] Sung Y-G., 2002, Modelling and control with piezo actuators for a simply supported beam under a moving mass, Journal of Sound and Vibration 250(4): 617-626.
[5] Nikkhoo A., Rofooei F. R., Shadnam M. R., 2007, Dynamic behavior and modal control of beams under moving mass, Journal of Sound and Vibration 306(3): 712-724.
[6] Prabakar R. S., Sujatha C., Narayanan S., 2009, Optimal semi-active preview control response of a half car vehicle model with magnetorheological damper, Journal of Sound and Vibration 326 (3): 400-420.
[7] Pisarski D., CzesŁaw I.B., 2010, Semi-active control of 1D continuum vibrations under a travelling load, Journal of Sound and Vibration 329(2): 140-149.
[8] Ryu B.J., Yong-Sik K., 2012, Dynamic Responses and Active Vibration Control of Beam Structures under a Travelling Mass, INTECH Open Access Publisher.
[9] Flanders S. W., Laura I.B., Melek Y., 1994, Alternate Neural Network Architectures for Beam Vibration Minimization, ASME-PUBLICATIONS-AD.
[10] Chen Ching I., Marcello R.N., James E.S., 1994, Active vibration control using the modified independent modal space control (MIMSC) algorithm and neural networks as state estimators, Journal of Intelligent Material Systems and Structures 5(4): 550-558.
[11] Smyser C.P., Chandrashekhara K., 1997, Robust vibration control of composite beams using piezoelectric devices and neural networks, Smart Materials and Structures 6(2): 178.
[12] Valoor Manish T., Chandrashekhara K., Sanjeev A., 2001, Self-adaptive vibration control of smart composite beams using recurrent neural architecture, International Journal of Solids and Structures 38(44): 7857-7874.
[13] Qiu Zh., Xiangtong Zh., Chunde Y., 2012, Vibration suppression of a flexible piezoelectric beam using BP neural network controller, Acta Mechanica Solida Sinica 25(4): 417-428.
[14] Ku Chao Ch., Kwang Y.L., 1995, Diagonal recurrent neural networks for dynamic systems control, IEEE Transactions on Neural Networks 6(1): 144-156.
[15] Li X., Wen Y., 2002, Dynamic system identification via recurrent multilayer perceptrons, Information Sciences 147(1): 45-63.
[16] Lin F-J., Hsin-Jang Sh., Po-Huang Sh., Po-Hung Sh., 2006, An adaptive recurrent-neural-network motion controller for XY table in CNC machine, IEEE Transactions on Systems, Man, and Cybernetics, Part B 36(2): 286-299.
[17] Lin F-J., Hsin-Jang Sh., Li-Tao T., Po-Huang Sh., 2005, Hybrid controller with recurrent neural network for magnetic levitation system, IEEE Transactions on Magnetics 41(7): 2260-2269.
[18] Pearlmutter Barak A., 1989, Learning state space trajectories in recurrent neural networks, Neural Computation 1(2): 263-269.
[19] Yu W., 2004, Nonlinear system identification using discrete-time recurrent neural networks with stable learning algorithms, Information Sciences 158: 131-147.
[20] Haykin S., 1998, Neural Networks: A Comprehensive Foundation, Prentice Hall PTR.
[21] Kasparian V., Celal B., 1998, Model reference based neural network adaptive controller, ISA Transactions 37(1): 21-39.