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A discrete model of a rope with bending stiffness or viscous damping

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Abstract

A discrete model of a rope is developed and used to simulate the plane motion of the rope fixed at one end. Actually, two systems are presented, whose members are rigid but non-ideal joints involve elasticity or dissipation. The dissipation is reflected simply by viscous damping model, whereas the bending stiffness conception is based on the classical curvature-bending moment relationship for beams and simple geometrical formulas. Equations of motion are derived and their complexity is discussed from the computational point of view. Since modified extended backward differentiation formulas (MEBDF) of Cash are implemented to solve the resulting initial value problems, the technique scheme is outlined. Numerical experiments are performed and influences of the elasticity and damping on behaviour of the model are analyzed. Basic energy principles are used to verify the obtained results.

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References

  1. McLachlan, N.: Całki iloczynów dwóch funkcji Bessela-zastosowania. In: Funkcje Bessela dla in żynieróow, chap. 5, 149–154. PWN (1964)

    Google Scholar 

  2. Goriely, A., McMillen, T.: Shape of a cracking whip. Physical Review Letters 88(24), 244301-1–4 (2002)

    Article  Google Scholar 

  3. McMillen, T., Goriely, A.: Whip waves. Physica D 184, 192–225 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gatti, C., Perkins, N.: Physical and numerical modeling of the dynamic behavior of a fly line. Journal of Sound and Vibration 255(3), 555–577 (2002)

    Article  Google Scholar 

  5. Jimenez, J., Hernandez, G., Campos, I., et al.: Newtonian and canonical analysis of the motion of a rope falling from a table. Eur. J. Phys. 26, 1127–1137 (2005)

    Article  MATH  Google Scholar 

  6. Wong, C., Yasu, K.: Falling chains. Physical Review Letters 74(6), 490–496 (2006)

    Google Scholar 

  7. Yong, D.: Strings, chains and ropes. SIAM Review 48(4), 771–781 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Pierański, P., Tomaszewski, W.: Dynamics of ropes and chains: I. the fall of the folded chain. New Journal of Physics 7(45) (2005)

  9. Tomaszewski, W., Pierański, P., Geminard, J.: The motion of the freely falling chain tip. Am. J. Phys. 74, 776–783 (2006)

    Article  Google Scholar 

  10. Fritzkowski, P., Kamiński, H.: Dynamics of a rope as a rigid multibody system. Journal of Mechanics of Materials and Structures 3(6), 1059–1075 (2008)

    Article  Google Scholar 

  11. Fritzkowski, P., Kamiński, H.: Dynamics of a rope modeled as a discrete system with extensible members. Computational Mechanics 44(4), 473–480 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cash, J.R.: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations. In: Proc. R. Soc. Lond. A 459, 797–815 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cash, J.R.: Modifed extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs. Journal of Computational and Applied Mathematics 125, 117–130 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Cash, J.R., Considine, S.: An MEBDF Code for Stiff Initial Value Problems. ACM Transactions on Mathematical Software 18(2), 142–155 (1992)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mechanics, Poznan University of Technology, Piotrowo 3, 60-965, Poznan, Poland

    Pawel Fritzkowski & Henryk Kaminski

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  1. Pawel Fritzkowski
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  2. Henryk Kaminski
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Correspondence to Pawel Fritzkowski.

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Fritzkowski, P., Kaminski, H. A discrete model of a rope with bending stiffness or viscous damping. Acta Mech Sin 27, 108–113 (2011). https://doi.org/10.1007/s10409-011-0417-0

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  • DOI: https://doi.org/10.1007/s10409-011-0417-0

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