Skip Navigation Links
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


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:

Vibratory Forces and Their Influence on Mechanical Systems

Journal of Applied Nonlinear Dynamics 11(3) (2022) 533--547 | DOI:10.5890/JAND.2022.09.003

Tadeusz Majewski

Industrial and Mechanical Engineering Department, Universidad de las Am\'{e}ricas Puebla, 72810, Mexico

Download Full Text PDF



Several types of vibrating systems experiencing some interesting effects of inertial forces generated by vibrations are studied. The behavior of these systems can be easily predicted when we know how and which vibratory forces are affecting them. One example is a pendulum with a vibrating pivot that changes the position of equilibrium, alters the natural frequency, and the vibratory force stabilizes its inverse position. Sometimes, a rotor might not reach the final velocity due to the resonance because of the breaking vibratory moment, or the rotor speed decreases rapidly if the motor is switched off. If the imbalanced rotor has free elements inside it, then they can freely align their position and compensate the initial rotor imbalance. Also, the free elements of the rotor are able to eliminate its vibration if the rotor is placed on a vibrating base. It is observed that it is easier to move an object if it is on a vibrating surface than when the surface is not moving at all, apparently due to a lower friction force. By controlling the vibration components of the plane, the object's trajectory as well as its velocity can be controlled. This model can be used to simulate the locomotion of living systems or active Brownian particles.\newline A novel method of analysing mechanical systems which allows to explain their dynamic behaviour and allows to predict some effects is described, along with some examples of laboratory tests.


  1. [1]  Blekhman, I. (2000), Vibrational Mechanics, Nonlinear Dynamic Effects, General Approach, Applications, World Scientific, Singapore,
  2. [2]  Biewener, A.A. (2003), Animal Locomotion, Oxford Animal Biology Series.
  3. [3]  Alexander, R.M. (2003), Principles of Animal Locomotion, Princeton University Press, New Jersey.
  4. [4]  Handbooks of Robotics, Chapter 61, Biologically-inspired robots, Agnes Guillot, 2007.
  5. [5]  Huygens, C. (1673), Letter to the Royal Society of London.
  6. [6]  Blekhman, I. (1971), Synchronization of Mechanical Systems, (in Russian), Nauka, Moscu.
  7. [7]  Rosenblum, M. and Pikovsky, A. (2003), Synchronization: from pendulum clocks to chaotic lasers and chemical oscillators, Contemporary Physics, 44(5), 401-416, DOI:10.1080/00107510310001603129.
  8. [8]  Czolczynski, K., Perlikowski, P., Stefanski, A., and Kapitaniak, T. (2012), Synchronization of slowly rotating pendulums, Int. J. Bifurcation and Chaos, 22(5),
  9. [9]  Bogusz, W. and Engel, Z. (1965), Investigation of a system for contactless transmission of power (in Polish), Science-technical information, HPR 20.
  10. [10]  Boda, Sz., Neda, Z., Tyukodi, B., and Tunyagi, A. (2013), The rhythm of coupled metronome, Eur. Phys. J. B, 86(263), DOI:10.1140/epjb/e2013-31065-9.
  11. [11]  Sado, D. (2010), Regular and chaotic vibrations in some systems with the pendulums, (in Polish), Wydawnictwa Naukowo Techniczne, Warsaw.
  12. [12]  Carranza, J.C., Brennan, M.J., and Tang, B. (2016), On the synchronization of two metronomes and their related dynamics, Journal of Physics: Conference Series, 744, 012133, DOI:10.1088/1742-6596/744/1/012133.
  13. [13]  Majewski, T., Domagalski, R., and Meraz, M. (2007), Dynamic compensation of dynamic forces in two planes for the rigid rotor, Journal of Theoretical and Applied Mechanics, 45(2), 379-403.
  14. [14]  Majewski, T., Szwedowicz, D., and Herrera, A. (2011), Automatic elimination of vibrations for a centrifuge, Mechanism and Machine Theory, 46(3), 344-357.
  15. [15]  Majewski, T., Szwedowicz, D., and Meraz Melo, M. (2015), Self-balancing system of the disk on an elastic shaft, Journal of Sound and Vibration, 359, 2-20, DOI:10.1016/j.jsv.2015.06.035.
  16. [16]  Majewski, T. (2000), Synchronous Elimination of Vibrations in the Plane. Analysis of Occurrence of Synchronous Movements, Journal of Sound and Vibration, No. 232-2, pp.553-570.
  17. [17]  Majewski, T. (2008), Resultant friction for a system with vibration, Machine Dynamics Problems, 32(2), 38-48.
  18. [18]  Majewski, T., Szwedowicz, D., and Majewski, M. (2017), Locomotion of a mini bristle robot with inertial excitation, Journal of Mechanisms and Robotics, 9(6), 061008-1061008-11, DOI:10.1115/1.4037892.
  19. [19]  Junot, G., Briand, G., Ledesma-Alonso, R., and Dauchot, O. (2017), Active versus passive hard disks against a membrane: Mechanical pressure and instability, Phys. Rev. Lett., 119, 028002.
  20. [20]  Deseigne, J., Leonard, S., Dauchot, O., and Chate, H. (2012), Vibrated polar disks: spontaneous motion, binary collisions, and collective dynamics, Soft Matter, 8, 5629.
  21. [21]  Bajkowski, J.M., Dyniewicz, B., Bajer, C.I., and Bajkowski, J. (2020), An experimental study on granular dissipation for the vibration attenuation of skis, Proceedings of the Institution of Mechanical Engineers, Part P: J Sports Engineering and Technology, DOI:10.1177/1754337120964015).