Abstract
Background
In recent years, interesting results have been obtained on the study of the nonlinear dynamics of translational, rotational and pendulum electromechanical systems. Most of these systems consider one-directional motions or coupling of one-directional motions. However, for some applications, actuators can move over different places on a surface or plane.
Purpose
The purpose of this work is to study the nonlinear dynamics of a mass moving over a plane when it is subjected to perpendicular springs and perpendicular forces created two periodically excited electromagnets with phase shift.
Methods
After the derivation of the equations of motions using mechanics laws and interaction forces created by electromagnets, the harmonic balance method and the fourth-order Runge-Kutta method are used to obtain mathematically and numerically the dynamical states of the system.
Results
It is found that a bidimensional periodic motion takes place along the oblique line with slope depending on the phase shift. The frequency-response curves of the periodic motion show resonance, antiresonance and hysteresis. The bifurcation diagrams versus the amplitude of the excitations and the phase shift show that the dynamical states can be periodic or chaotic. The transition from the periodic states to chaos is either through successive period-doublings or abrupt.
Conclusion
In this work, the nonlinear dynamics of a mass subjected to the action of perpendicular springs and perpendicular periodic forces with phase shift has been analyzed. It has been found that the mass can exhibit several dynamical states in a plane including chaos characterized by the random distribution of the positions occupied by the mass in the bidimensional space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Not applicable.
References
Mbou-Soh GB, Monkam YJ, Nwagoum-Tuwa PR, Tchinga R, Woafo P (2020) Study of a piezoelectric plate based self-sustained electric and electromechanical oscillator. Mech Res Commun 105:103504
Kuhnert WM, Cammarano A, Silveira M (2021) Synthesis of viscoelastic behavior through electromechanical coupling. J Vib Eng Technol 9:367–379. https://doi.org/10.1007/s42417-020-00235-0
Luo S, Lewis F, Song Y, Garrappa R (2021) Dynamical analysis and accelerated optimal stabilization of the fractionalorder self-sustained electromechanical seismograph system with fuzzy wavelet neural network. Nonlinear Dyn 104:1389–1404
Litak G, Syta A, Wasilewski G, Kudra G, Awrejcewicz J (2020) Dynamical response of a pendulum driven horizontally by a dc motor with a slider-crank mechanism. Nonlinear Dyn 99:1923–1935
Hedjar R, Bounkhel M (2014) Real-time obstacle avoidance for as warm of autonomous mobile robots. Chaos Solit Fract 11:53–62
Olímpio P, de-Sá-Neto AS, Helder-Costa F (2019) Estimation of decoherence in electromechanical circuits. Phys Lett A 383(31):1–4
Ji JC (2003) Stability and bifurcation in an electromechanical system with time delay. Mech Res Commun 30:217–225
Kitio-Kwuimy CA, Woafo P (2010) Experimental realization and simulations a self-sustained macro-electromechanical system. Mech Res Commun 37:106–110
Sabarathinam S, Thamilmaran K (2017) Implementation of analog circuit and study of chaotic dynamics in à generalized Duffing-type MEMS resonator. Nonlinear Dyn 87:2345–2356
DeMartini BE, Butterfield HE, Moehlis J, Turner KL (2007) Chaos for a microelectromechanical oscillator governed by the nonlinear Mathieu equation. J Microelectromech Syst 16(6):1314–1323
Awrejcewicz J, Dzyubak L, Lamarque CH (2008) Modelling of hysteresis using Masing–Bouc–Wen’s framework and search of conditions for the chaotic responses. Commun Nonlinear Sci Numer Simul 13:935–958
Awrejcewicz J, Supel B, Lamrque CH, Kudra G, Wasilewski G, Olejnik P (2008) Numerical and experimental study of regular and chaotic motion of triple physical pendulum. Int J Bifurcat Chaos 10(18):2883–2915
Awrejcewicz J, Kudra G, Wasilewski G (2008) Chaotic zones in triple pendulum dynamics observed experimentally and numerically. Appl Mech Mater 9:1–17
Simo-Domguia U, Abobda LT, Woafo P (2016) Dynamical behavior of à capacitive microelectromechanical system powered by à Hindmarsh-Rose electronic oscillator. J Comput Non Dyn 11(5):1–7
Simo-Domguia U, Tchakui MV, Simo H, Woafo P (2017) Theoretical and experimental study of an electromechanical system actuated by à Brusselator electronic circuit simulator. J Vib Acoust 139(6):1–11
Kouam-Tagne RF, Tsapla-Fotsa R, Woafo P (2021) Dynamics of à DC Motor-Driving arm with à circular periodic potential and DC/AC volatage input. Int J Bifurc Chaos 31(12):1–19
Hedjar R, Bounkhel M (2014) Real-time obstacle avoidance for a swarm of autonomous mobile robots. Chaos Solit Fract 11:53–62
Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, Hoboken
Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
Author information
Authors and Affiliations
Contributions
USD: methodology, mathematical and numerical developments, writing of the original draft. PW: design the model—supervision of the study, review the writing of the manuscript.
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Domguia, U.S., Woafo, P. Dynamical Behaviors of a Mass Submitted to the Action of Perpendicular Spring and Excitations with Phase Shift. J. Vib. Eng. Technol. 12, 3897–3904 (2024). https://doi.org/10.1007/s42417-023-01093-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42417-023-01093-2