Skip Navigation Links
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


Electromagnetic Control of Nonlinear Behavior of an Excited Cantilever Beam in a Single Mode Approximation

Journal of Vibration Testing and System Dynamics 2(1) (2018) 1--8 | DOI:10.5890/JVTSD.2018.03.001

Amine Bichri$^{1}$, Jarir Mahfoud$^{2}$, Mohamed Belhaq$^{3}$

$^{1}$ Faculty of Science and Technology-Errachidia, Errachidia, Morocco

$^{2}$ INSA-Lyon, LaMCoS UMR5259, Lyon, France

$^{3}$ University Hassan II-Casablanca, Casablanca, Morocco

Download Full Text PDF



The effects of combined DC and fast AC electromagnetic actuations on the dynamic behavior of an excited cantilever beam is studied considering a single mode approximation. Analytical investigation is performed to extract the equation of motion describing the slow dynamic of the system. The influence of the fast AC actuation and the air gap on the nonlinear behavior of the system is examined. It is shown that the nonlinear characteristic of the system can be controlled by appropriately tuning the AC actuation or the air gap. This can be useful in certain engineering applications where the operating frequency range includes one or several critical frequencies that should be avoided.


  1. [1]  Schweitzer, G., Bleuler, H., and Traxler, A. (2003), Active Magnetic Bearings - Basics, Properties and Applications vdf Hochschulverlag AG, ETH, Zurich.
  2. [2]  Gutman, I. (1968), Industrial Uses of Mechanical Vibrations, Business Books Limited, London.
  3. [3]  Chang, H.T., Lee, C.Y., Wen, C.Y., and Hong, B.S. (2007), Theoretical analysis and optimization of electromagnetic actuation in a valveless microimpedance pump, Microelectronics Journal, 38, 791-799.
  4. [4]  Der Hagopian, J. and Mahfoud, J. (2010), Electromagnetic actuator design for the control of light structures, Smart Structures and Systems, 6, 29-38.
  5. [5]  Gospodaric, B., Voncina, D., and Bucar, B. (2007), Active electromagnetic damping of laterally vibrating ferromagnetic cantilever beam, Mechatronics, 17, 291-298.
  6. [6]  Mahfoud, J., Skladanek, Y., and Der Hagopian, J. (2011), Active control and energy cost assessment of rotating machine, Shock and Vibration, 18, 613-625.
  7. [7]  Jianfei, Y., Jinji, G. and Weimin, W. (2015), Multi-frequency rotor vibration suppressing through selfoptimizing control of electromagnetic force, Journal Vibration and Control, doi:1077546315586301.
  8. [8]  Dimitri, A.S., El-Shafei, A., Adly, A., and Mahfoud, J. (2015),Magnetic actuator control of oil whip instability in bearings, Magnetics, IEEE Transactions, PP99, 1-1, DOI: 10.1109/TMAG.2015.2456030. 2015.
  9. [9]  Askari, H. and Esmailzadeh, E. (2014), Free vibration of micro cantilever beam with electromagnetic actuators, Dynamics, Vibration and Control, ESDA2014-20569, V002T07A026.
  10. [10]  Przybylowicz, P.M. (2017), Near-Critical behavior of an elastic rotating shaft stabilized by electromagnetic actuators, Int. J. Str. Stab. Dyn., 0, 1740013.
  11. [11]  Belhaq, M., Bichri, A., Der Hogapian, J., and Mahfoud, J. (2011), Effect of electromagnetic actuations on the dynamics of a harmonically excited cantilever beam, International Journal of Non-Linear Mechanics, 46, 828-838.
  12. [12]  Bichri, A., Belhaq, M., and Mahfoud, J. (2014), Effect of high-frequency AC electromagnetic actuation on the dynamic of an excited cantilever beam, MATEC Web of Conferences, 16, 08002.
  13. [13]  Perret-Liaudet, J. and Rigaud, E. (2006), Response of an impacting hertzian contact to an order-2 subharmonic excitation: theory and experiments, J. Sound Vib, 296, 319-333.
  14. [14]  Blekhman, I.I. (2000), Vibrational Mechanics - Nonlinear Dynamic Effects, General Approach, Application, Singapore: World Scientific.
  15. [15]  Thomsen, J.J. (2003), Vibrations and Stability: Advanced Theory, Analysis, and Tools Springer, Berlin.
  16. [16]  Nayfeh, A.H. and Mook, D.T. (1979) Nonlinear Oscillations. Wiley, New York.