ABSTRACT This paper examines modelling of the dynamics of a plate by plate type dynamics vibration absorber subjected to a localized periodic impulsive excitation. An analytical solution of the modal equation is proposed and validated using direct numerical simulation of the basic equations. The basics equations are solve numerically using fourth order Runge Kutta algorithm. Various types of dynamic absorbing plate are tested to optimize the control efficiency. Particular attentions have been paid on the effects of localization of external forces on the dynamics response of the system under control. Ours findings demonstrate that a good achievement of control strategy should follow the above mentioned analysis.
Cite this paper
nullH. Bouna and B. Nbendjo, "Vibration Control of a Plate Subjected to Impulsive Force by Plate-Type Dynamic Vibration Absorbers," World Journal of Mechanics, Vol. 2 No. 3, 2012, pp. 143-151. doi: 10.4236/wjm.2012.23017.
 T. T. Song and W. F. Chen, “Active Structural Control: Theory and Practice,” Wiley, New York, 1990.
 C. R. Fuller, S. J. Eliot and P. A. Nelson, “Active Control of Vibration,” Academic Press, London, 1997.
 S. H. Kim, S. B. Choi, S. R. Hang and M. S. Han, “Vibration Control of Fexible Structure Using a Hybrid Mounts,” International Journal of Mechanical Sciences, Vol. 46, No. 1, 2004, pp. 143-157.
 L. Jezequel, “Active Control in Mechanical Engineering,” Hermes, New Castle, 1995.
 B. R. Nana Nbendjo and P. Woafo, “Modelling, Control by Sandwich of the Dynamics and Optimization in a Strongly Nonlinear Beam,” Far East Journal of Dynamical Systems, Vol. 8, 2006, pp. 267-283.
 T. Aida, K. Kawazoe and S. Toda, “Vibration Control of Plates by Plate-Type Dynamics Vibration Absorber,” Journal of Vibration and Acoustics, Vol. 117, No. 3, 1995, pp. 332-338. doi:10.1115/1.2874455
 T. Aida, S. Toda, S. N. Ogowa and Y. Simada, “Vibration Control of Beams by Beam Type Dynamics Vibrations Absorber,” ASCE Journal of Engineering Mechanics, Vol. 118, No. 2, 1992, pp. 163-175.
 B. R. Nana Nbendjo and P. Woafo, “Modeling and Optimal Active Control with Delay of the Dynamics of a Strongly Nonlinear Beam,” Journal of Advanced Research in Dynamical and Control Systems, Vol. 1, 2009, pp. 57-74.
 C. A. Kitio Kwuimy, B. R. Nana Nbendjo and P. Woafo, “Optimization of Electromechanical Control of Beam Dynamics: Analytical Method and Finite Differences Simulation,” Journal of Sound and Vibration, Vol. 298, No. 1-2, 2006, pp. 180-193. doi:10.1016/j.jsv.2006.05.019
 A. A. Nanha Djanan, B. R. Nana Nbendjo and P. Woafo, “Control of Vibration on a Hinged-Hinged Beam under a Non-Ideal Excitation Using RLC Circuit with Variable Capacitance,” Nonlinear Dynamics, Vol. 63, No. 3, 2011, pp. 477-489. doi:10.1007/s11071-010-9816-1
 J. L. P. Felix and J. M. Balthazar, “Comments on a Non-linear and Non-Ideal Electromechanical Damping Vibration Absorber, Sommerfeld Effect and Energy Transfer,” Nonlinear Dynamics, Vol. 55, No. 1-2, 2009, pp. 1-11.
 R. A. Morgan and R. W. Wang, “An Active Passive Piezoelectric Absorber for Structural Vibration Control under Harmonic Excitations with Time-Varying Frequency, part1: Algorithm Development and Analysis,” Journal of Vibration and Acoustics, Vol. 124, No. 1, 2002, pp. 77-83.
 M. S. Tsai and K. W. Wang, “On the Structural Damping Characteristics of Active Piezoelectric Actuator with Pas- sive Shunt,” Journal of Sound and Vibration, Vol. 221, No. 1, 1999, pp. 1-22. doi:10.1006/jsvi.1998.1841
 I. Bica, “Damper with Magnetorheological Suspension,” Journal of Magnetism and Magnetic Materials, Vol. 241, No. 2-3, 2002, pp. 196-200.
 B. Liu and H. S. Tzou, “Distributed Photostrictive Actuator and Optopiezothermoelasticity Applied to Vibration Control of Plates,” Journal of Vibration and Acoustics, Vol. 120, No. 4, 1998, pp. 936-943.
 H.-R. Shih, H.-S. Tzou and M. Saypuri, “Structural Vibration Control Using Spacially, Configured Opto-Electro- mechanical Actuators,” Journal of Sound and Vibration, Vol. 284, No. 1-2, 2005, pp. 361-378.
 Q. Zhang and B. Z. Guo, “Stabilization of an Elastic Plate with Viscoelastic Boundary Conditions,” Journal of Optimization Theory and Application, Vol. 122, No. 3, 2004, pp. 669-690. doi:10.1023/B:JOTA.0000042600.95607.f9
 H. P. Niu, Y. H. Zhang, X. H. Zhang and S. L. Xie, “Active Vibration Control of Plates Using Electro-Magnetic Constrained Layer Damping,” International Journal of Applied Electromagnetics and Mechanics, Vol. 33, No. 1, 2010, pp. 831-837.
 S. Lenci and G. Rega, “Periodic Solutions and Bifurcations in an Impact Inverted Pendulum under Impulsive Excitation,” Chaos, Solitons and Fractals, Vol. 11, No. 15, 2000, pp. 2453-2472.
 D. Zwillinger, “Handbook of Differential Equations,” 3rd Edition, Academic Press, Cambridge, 1997.