Skip to main content

Advertisement

SpringerLink
Log in

Two parametric excited nonlinear systems due to electromechanical coupling

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

This paper analyzes the behavior of two electromechanical systems. In the first part of the work, a simple system is analyzed. It is composed of a cart, whose motion is excited by a DC motor (motor with continuous current). The coupling between the motor and the cart is made by a mechanism called scotch yoke, so that the motor rotational motion is transformed in horizontal cart motion over a rail. The developed model of the system takes into account the influence of the DC motor in the dynamic behavior of the system. It is formulated as an initial value problem, in which the coupling torque between the mechanical and electric systems appears as a parametric excitation. By simulations, it is verified that the system has a periodic solution with a relation 2:1 between the period of rotation of the disk (part of the electromechanical system) and the period of the current in the DC motor. In the second part of the work, a pendulum is embarked into the cart. Its suspension point is fixed in cart, so that there exists a relative motion between the cart and the pendulum. The excitation of the pendulum comes from the motion of the cart, so it is not controlled and can vary widely because the pendulum can store energy. The pendulum acts as a hidden parameter of the system. The influence of the embarked pendulum in the dynamic behavior of the system is investigated and it is shown how it can affect the solutions of the dynamic equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

  1. Aguiar R (2010) Experimental investigation and numerical analysis of the vibro-impact phenomenon. Ph.D. thesis, PUC-Rio, Rio de Janeiro, Brazil

  2. Aguiar R, Weber HI (2012) Impact force magnitude analysis of an impact pendulum suspended in a vibrating structure. Shock Vib 19:1359–1372

    Article  Google Scholar 

  3. Aguiar R, Weber HI (2011) Mathematical modeling and experimental investigation of an embedded vibro-impact system. Nonlinear Dyn 65:317–p334

    Article  Google Scholar 

  4. Balthazar J, Mook D, Weber H, Brasil R, Felini A, Belato D, Felix J (2003) An overview on non-ideal vibrations. Meccanica 38:613–621

    Article  MATH  Google Scholar 

  5. Belato D (2002) Análise Não Linear de Sistemas Dinâmicos Holônomos Não Ideais, PhD thesis, Department of Mechanical Engineering, Universidade Estadual de Campinas, Campinas, S.P., Brazil

  6. Cartmell M (1990) Introduction to Linear, parametric and nonlinear vibrations. Chapman and Hall, New York

    MATH  Google Scholar 

  7. Dantas MJH, Sampaio R, Lima R (2014) Stable periodic orbits of a coupled electromechanical system. Nonlinear Dyn 78(1):29–35

    Article  Google Scholar 

  8. Cataldo E, Bellizzi S, Sampaio R (2013) Free vibrations of an uncertain energy pumping system. J Sound Vib 332:6815–6828

    Article  Google Scholar 

  9. Evan-Iwanowski RM (1976) Resonance oscillations in mechanical systems. Elsevier's Scientific Publishing Company, Amsterdam

    MATH  Google Scholar 

  10. Fidlin A (2006) Nonlinear oscillations in mechanical engineering. Springer, Netherlands

    Google Scholar 

  11. Gourdon E (2006) Contrôle Passif de Vibrations par Pompage Énergétique. Ph.D. thesis, Ecole Centrale de Lyon

  12. Gourdon E, Alexander N, Taylor C, Lamarque C, Pernot S (2007) Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: theoretical and experimental results. J Sound Vib 300:522–551

    Article  Google Scholar 

  13. Hagedorn P (1988) Non-linear oscillations. In: 2nd edn, Oxford University Press, Oxford

  14. Karnopp D, Margolis D, Rosenberg R (2006) System dynamics: modeling and simulation of mechatronic systems. In: 4th edn, John Wiley and Sons, Hoboken, New Jersey

  15. Kononenko VO (1969) Vibrating systems with a limited power supply. London Iliffe Books LTD, England

    Google Scholar 

  16. Lacarbonara W, Antman S (2008) What is parametric excitation in structural dynamics? ENOC-2008, Saint Petersburg, Russia

    Google Scholar 

  17. Lee HS, Incheon I, Cho C, Chang SP (2006) Design and analysis of electro-mechanical characteristics of micromachined stainless steel pressure sensor. In: Proceedings of the 5th IEEE Sensors Conference, IEEE Sensors, South Korea, pp 659–674

  18. Luo ACJ, Yu B (2014) Analytical solutions of period-m motions in a parametric, quadratic nonlinear oscillator. ENOC-2014, Vienna, Austria

  19. Lima R, Sampaio R (2012) Stochastic analysis of an electromechanical coupled system with embarked mass. Mecânica Comput: XXXI, pp 2783–2800. http://www.cimec.org.ar/ojs/index.php/mc/article/view/4216/4142

  20. Nayfeh AH, Mook DT (1979) Nonlinear oscillations. John Wiley and Sons, New York, USA

    MATH  Google Scholar 

  21. Neumeyer S, Looij R, Thomsen JJ (2014) Jumps and bi-stability in the phase-gain characteristics of a nonlinear parametric amplifier. ENOC-2014, Vienna, Austria

    Google Scholar 

  22. Peruzzi NJ, Chavarette FR, Balthazar JM, Manfrim ALP, Brasil R.M.F.L. (2014) On control of a parametrically excited time-periodic “mems”. ENOC-2014, Vienna, Austria

  23. Rocard Y (1943) Dynamique générale des vibrations. Masson et Cie Éditeurs, Paris, France

    MATH  Google Scholar 

  24. Sadeghian H, Rezazadeh G (2009) Comparison of generalized differential quadrature and Galerkin methods for the analysis of micro-electro-mechanical coupled systems. Commun Nonlinear Sci Numer Simul 14:2807–2816

    Article  Google Scholar 

  25. Sorokin V (2014) On the response of a nonlinear parametric amplifier driven beyond resonance. ENOC-2014, Vienna, Austria

    Google Scholar 

  26. Troger H, Steindl A (1991) Nonlinear stability and bifurcation theory: an introduction for engineers and applied scientists. Springer-Verlag, Wien

    Book  MATH  Google Scholar 

  27. Warminski J, Balthazar JM (2003) Vibrations of a parametrically and self-excited system with ideal and non-ideal energy sources. J Braz Soc Mech Sci Eng 25(4): pp 413–420

  28. Zhankui S, Sun K (2013) Nonlinear and chaos control of a micro-electro-mechanical system by using second-order fast terminal sliding mode control. Commun Nonlinear Sci Numer Simul 18:2540–2548

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the Brazilian Agencies CNPQ, CAPES and Faperj.

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, PUC-Rio, Rio de Janeiro, Brazil

    Roberta Lima & Rubens Sampaio

Authors
  1. Roberta Lima
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rubens Sampaio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roberta Lima.

Additional information

Technical Editor: Fernando Alves Rochinha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lima, R., Sampaio, R. Two parametric excited nonlinear systems due to electromechanical coupling. J Braz. Soc. Mech. Sci. Eng. 38, 931–943 (2016). https://doi.org/10.1007/s40430-015-0395-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-015-0395-4

Keywords

Search

Navigation