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Influence of some speed parameters on the dynamics of nonlinear flexural vibrations of a drill column

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Języki publikacji
EN
Abstrakty
EN
We investigate the influence of the motion of fluid flushing the cutter of a well drilling column, and the angular rotational velocity upon dynamic characteristics of its flexural vibrations. We take into account the nonlinear elastic features of column material. As a base of the research we took the Galerkin method and the Van der Pol method. Combining those two methods made possible to obtain the relations describing the main parameters of the dynamical process In both nonresonance and resonance case.
Twórcy
autor
  • Department of Higher Mathematics, Lviv Polytechnic National University
autor
  • Department of Mechanics and Mechanical Engineering Automation, Lviv Polytechnic National University
autor
  • Department of Higher Mathematics, Lviv Polytechnic National University
Bibliografia
  • 1. Gashchuk P. М. and Nazar I. I. 2008. Influence of driving force on the self-reactance vibrations of flexible working element of mechanical occasion. Dynamics and strength of machines, no. 614, Lviv Polytechnic National University, Lviv, Ukraine, 55–65.
  • 2. Gashchuk P. М. and Nazar I. I. 2008. Self-reactance indignation of flexible working element of mechanical occasion. Ukrainian interdepartmental scientific and technical collection "Automation of productive processes in mechanical engineering", Issue 42, 65–69.
  • 3. Lavrenyuk S. P. and Pukach P. Ya. 2007. Mixed problem for a nonlinear hyperbolic equation in a domain unbounded with respect to space variables. Ukrainian Mathematical Journal, Volume 59, no. 11, 1708 – 1718.
  • 4. Shevchenko F. L. and Pettik Yu. V. 2010. Influence of speed of aleak liquid on stability of drilling column. Scientific herald of National Mining University, no. 1, 69–72.
  • 5. Ulitin G. М. 2000. Shock processes in boring settings. Vibrations in a technique and technologies, no. 1 (13), 70–74.
  • 6. Sokil B.I. 2001. Nonlinear vibrations of mechanical systems and analytical methods for their research. Abstract of Dr. Sci. (Tech.) dissertation, Dynamics and strength of machines, Lviv Polytechnic National Univ., Lviv, Ukraine, 24 p.
  • 7. Chen L. Q. 2005. Analysis and control of transverse vibrations of axially moving strings. Appl. Mech. Rev, Volume 58, 91–116.
  • 8. Pukach P. Ya. 2006. Mixed problem for some nonlinear equation of beam vibrations type in bounded domain. Applied problems of mechanics and mathematics, Issue 4, 59-69.
  • 9. Pukach P. Ya. 2007. Mixed problem for nonlinear equation of beam vibrations type in unbounded domain. Matematychni Studii, Volume 27, no. 2, 139-148.
  • 10. P. Pukach, I. Kuzio and M. Sokil. 2013. Qualitative methods for research of transversal vibrations of semiinfinite cable under the action of nonlinear resistance forces. ECONTECHMOD, Volume 2, Issue 1, 43-48.
  • 11. Pukach P. Ya. 2004. Mixed problem in unbounded domain for weakly nonlinear hyperbolic equation with growing coefficients. Matematychni metody i fizykomekhanichni polya, Volume 47, no. 4, 149 - 154.
  • 12. Salenger G. and Vakakis A.F. 1998. Discreteness effects in the forced dynamics of a string on a periodic array of non-linear supports. Int. Journ. Non-Lin. Mech. Volume 33, 659 - 673.
  • 13. Santee D.M. and Goncalves P.B. 2006. Oscillations of a beam on a non-linear elastic foundation under periodic loads. Shock and Vibrations, Volume 13, 273 -284.
  • 14. Demeio L. and Lenci S. 2007. Forced nonlinear oscillations of semi-infinite cables and beams resting on a unilateral elastic substrate. Nonlinear Dynamics, Volume 49, 203 - 215.
  • 15. Demeio L. and Lenci S. 2008. Second-order solutions for the dynamics of a semi-infinite cable on a unilateral substrate. Journ. Sound Vibr., Volume 315, 414 - 432.
  • 16. Ghayesh M.H. 2010. Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation. Int. Journ. Non-Lin. Mech. Volume 45, 382 - 394.
  • 17. Lavrenyuk S. P. and Pukach P. Ya. 2007. Mixed problem for a nonlinear hyperbolic equation in a domain unbounded with respect to space variables. Ukrainian Mathematical Journal, Volume 59, no. 11, 1708 - 1718.
  • 18. Metrikine A.V. 2004. Steady state response of an infiniti string on a non-linear visco-elastic foundation to moving point loads. Journ. Sound Vibr., Volume 272, 1033 - 1046.
  • 19. Pecher H. 2000. Sharp existence results for self – similar solutions of semilinear wave equations. Nonlin. Diff. Equat. And Appl., Volume 7, 323 - 341.
  • 20. Mitropolski Yu. O. and Moseenkov B.I. 1976. Asymptotic solutions of partial differential equations. Vyshcha shkola, Kiev, 596 p.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0e345355-c55b-46c0-b2e0-b35284184803
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