Modification of the One-Parameter Numerical Continuation Method for Analysis of the Dynamics of Vibroimpact Systems

The modification of the one-parameter numerical continuation method for studying the dynamics of vibroimpact systems subject to periodic external loads is proposed. The behavior of a vibroimpact double spring mass system with two degrees of freedom is analyzed in relation to the load intensity. Specific applications of the method are compared with the two impact simulation procedures: contact force on the basis of the Hertz quasistatic theory and boundary conditions using the coefficient of restitution based on the stereomechanical theory of impact. Numerical analysis results for dynamic system states with the two impact simulation procedures are presented.

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References

  1. 1.

    V. I. Shalashilin and E. B. Kuznetsov, One-Parameter Numerical Continuation Method and the Best Parametrization [in Russian], Editorial URCC, Moscow (1999).

    Google Scholar 

  2. 2.

    E. L. Allgower and K. Georg, Introduction to Numerical Continuation Methods, Springer-Verlag, Berlin–New York (1990).

    Google Scholar 

  3. 3.

    V. I. Gulyaev, V. A. Bazhenov, E. S. Dekhtyaryuk, et al., Stability of Periodic Oscillation Modes in Nonlinear Mechanical Systems [in Russian], Vyshcha Shkola, Lvov (1983).

    Google Scholar 

  4. 4.

    V. A. Bazhenov, E. A. Gotsulyak, G. S. Kondakov, and A. I. Ogloblya, Stability and Oscillations of Deformable Systems with Unilateral Constraints [in Russian], Vyshcha Shkola, Kiev (1989).

    Google Scholar 

  5. 5.

    E. S. Dekhtyaryuk, O. S. Pogorelova, T. G. Postnikova, and S. M. Goncharenko, “Stability of steady-state oscillation modes of the vibroimpact systems under periodic loading,” in: Strength of Materials and Theory of Constructions [in Ukrainian], Issue 69, Kyiv (2001), pp. 10–18.

  6. 6.

    E. S. Dekhtyaryuk, O. S. Pogorelova, T. G. Postnikova, and S. M. Goncharenko, “Numerical methods of construction of amplitude vs frequency characteristics of periodic oscillation modes of vibroimpact systems,” in: Strength of Materials and Theory of Constructions [in Ukrainian], Issue 70, Kyiv (2002), pp. 69–81.

  7. 7.

    E. S. Dekhtyaryuk, O. S. Pogorelova, T. G. Postnikova, and S. M. Goncharenko, “Analysis of steady vibroimpact processes in elastic systems on the internal impact contact,” in: Strength of Materials and Theory of Constructions [in Ukrainian], Issue 73, Kyiv (2003), pp. 31–44.

  8. 8.

    V. A. Bazhenov, O. S. Pogorelova, T. G. Postnikova, and S. N. Goncharenko, “Comparative analysis of modeling methods for studying contact interaction in vibroimpact systems,” Strength Mater., 41, No. 4, 392–398 (2009).

    Article  Google Scholar 

  9. 9.

    V. A. Bazhenov, O. S. Pogorelova, T. G. Postnikova, and O. A. Luk’yanchenko, “Numerical investigations of the dynamic processes in vibroimpact systems in modeling impacts by a force of contact interaction,” Strength Mater., 40, No. 6, 656–662 (2008).

    Article  Google Scholar 

  10. 10.

    O. S. Pogorelova and T. G. Postnikova, “Application of different impact simulation procedures for vibroimpact systems with inelastic and elastic limiters,” in: Strength of Materials and Theory of Constructions [in Ukrainian], Issue 86, Kyiv (2010), pp. 87–93.

  11. 11.

    W. Goldsmith, Impact: The Theory and Physical Behaviour of Colliding Solids, Edward Arnold, London (1960).

    Google Scholar 

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Correspondence to V. A. Bazhenov.

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Translated from Problemy Prochnosti, No. 6, pp. 101 – 110, November – December, 2014.

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Bazhenov, V.A., Pogorelova, O.S. & Postnikova, T.G. Modification of the One-Parameter Numerical Continuation Method for Analysis of the Dynamics of Vibroimpact Systems. Strength Mater 46, 801–809 (2014). https://doi.org/10.1007/s11223-014-9614-y

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Keywords

  • vibroimpact motion
  • impact simulation
  • contact force
  • coefficient of restitution
  • one-parameter numerical continuation method