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An Investigation into the Dynamic Interaction Between an Electro-dynamic Shaker and a Test Structure with Cubic Nonlinearity

  • Gianluca Gatti
  • Michael J. Brennan
  • Ivana Kovacic
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 168)

Abstract

This chapter describes the dynamic behaviour of a coupled system where a nonlinear oscillator is attached and driven harmonically by an electro-dynamic shaker. The shaker is modelled as a linear single degree-of-freedom oscillator and the nonlinear attachment is modelled as a hardening Duffing oscillator. The attachment consists of four elastic wires, represented as springs, and its nonlinearity is due to the geometric configuration of the springs, which incline as they extend. The mass of the nonlinear system is much less than the moving mass of the shaker so that the nonlinear system has little effect on the shaker dynamics. The objective is to explore the dynamic behaviour of this system under a range of different conditions. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the shaker such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the shaker. It is found that for some values of the system parameters a two-part frequency response curve can occur: a closed detached curve can appear as a part of the overall amplitude-frequency response, and this detached curve can lie outside or inside the main continuous resonance curve.

References

  1. 1.
    Nayfeh, A.H.: Nonlinear Interactions: Analytical Computational and Experimental Methods. Wiley, New York (2000)Google Scholar
  2. 2.
    Kovacic I, Brennan M.J. (eds): The Duffing Equation: Nonlinear Oscillators and Their Behavior. Wiley (2011)Google Scholar
  3. 3.
    Jiang, X., McFarland, M., Bergman, L.A., Vakakis, A.F.: Steady state passive nonlinear energy pumping in coupled oscillators: theoretical and experimental results. Nonlinear Dyn. 33, 87–102 (2003)CrossRefMATHGoogle Scholar
  4. 4.
    Starosvetsky, Y., Gendelman, O.V.: Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning. J. Sound Vib. 315, 746–765 (2008)CrossRefADSGoogle Scholar
  5. 5.
    Starosvetsky, Y., Gendelman, O.V.: Dynamics of a strongly nonlinear vibration absorber coupled to a harmonically excited two-degree-of-freedom system. J. Sound Vib. 312, 234–256 (2008)CrossRefADSGoogle Scholar
  6. 6.
    Starosvetsky, Y., Gendelman, O.V.: Vibration absorption in systems with a nonlinear energy sink: nonlinear damping. J. Sound Vib. 324, 916–939 (2009)CrossRefADSGoogle Scholar
  7. 7.
    Alexander, N.A., Schilder, F.: Exploring the performance of a nonlinear tuned mass damper. J. Sound Vib. 319, 445–462 (2009)CrossRefADSGoogle Scholar
  8. 8.
    Brennan, M.J., Gatti, G.: The characteristics of a nonlinear vibration neutralizer. J. Sound Vib. 331, 3158–3171 (2012)CrossRefADSGoogle Scholar
  9. 9.
    Hamdan, M.N., Burton, T.D.: On the steady state response and stability of non-linear oscillators using harmonic balance. J. Sound Vib. 166, 255–266 (1993)MathSciNetCrossRefADSMATHGoogle Scholar
  10. 10.
    Worden, K.: On jump frequencies in the response of the Duffing oscillator. J. Sound Vib. 198, 522–525 (1996)CrossRefGoogle Scholar
  11. 11.
    Brennan, M.J., Kovacic, I., Carrella, A., Waters, T.P.: On the jump-up and jump-down frequencies of the Duffing oscillator. J. Sound Vib. 318, 1250–1261 (2008)CrossRefADSGoogle Scholar
  12. 12.
    Gatti, G., Kovacic, I., Brennan, M.J.: On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator. J. Sound Vib. 329, 1823–1835 (2010)CrossRefADSGoogle Scholar
  13. 13.
    Gatti, G., Brennan, M.J.: On the effects of system parameters on the response of a harmonically excited system consisting of weakly coupled nonlinear and linear oscillators. J. Sound Vib. 330, 4538–4550 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Gianluca Gatti
    • 1
  • Michael J. Brennan
    • 2
  • Ivana Kovacic
    • 3
  1. 1.University of CalabriaRende (CS)Italy
  2. 2.Universidade Estadual PaulistaIlha Solteira (SP)Brazil
  3. 3.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

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