Coupled systems mechanics

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Analysis of 3D pendulum sliding along a rope

  • Ivica Kozar (Faculty of Civil Engineering, Radmile Matejcic 3)
  • Received : 2024.08.09
  • Accepted : 2024.10.30
  • Published : 2024.10.25
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Abstract

The paper deals with a dynamic engineering problem in which a mass attached to a pendulum slides along a cable. In this problem, the pendulum mass and the cable are coupled in a model described by a system of algebraic differential equations (DAE). In this paper, the formulation of the system of differential equations modelling the problem is presented together with the determination of the initial conditions. The developed model is general in the sense of a free choice of support location, elastic rope properties, pendulum length and the inclusion of braking forces. This model can be used in the design of real rope structures such as zip lines. Many calculated values that can be measured on a real structure can be exported from the model and used for parameter calibration. In one example, the model is related to a real rope structure to illustrate and validate the model. The most important aspect of the model is its ability to estimate the safety of a ropeway quickly and easily.

Keywords

Acknowledgement

This work was supported by projects uniri-tehnic-18-108-1245 and uniri-tehnic-23-176-3146, for which we gratefully acknowledge.

References

  1. Baillieul, J. (1985), "Kinematic programming alternatives for redundant manipulators", IEEE International Conference on Robotics and Automation, St. Louis, MO, USA. https://doi.org/10.1109/ROBOT.1985.1087234.
  2. Burov, A.A. and Nikonov, V.I. (2024), "Dynamics of a heavy pendulum of variable length with a movable suspension point", Acta Mechanica, 1-9. https://doi.org/10.1007/s00707-024-03926-x.
  3. Costa, L.G. and Savi, M.A. (2024), "Pendulum-based hybrid system for multidirectional energy harvesting", Nonlin. Dyn., 112(21), 18665-18684. https://doi.org/10.1007/s11071-024-10040-z.
  4. Coulibaly, J.B., Chanut, M.A., Lambert, S. and Nicot, F. (2018), "Sliding cable modeling: An attempt at a unified formulation", Int. J. Solid. Struct., 130, 1-10. https://doi.org/10.1016/j.ijsolstr.2017.10.025.
  5. Goldstein, H., Poole, C.P. and Safko, J.L. (2001), Classical Mechanics, Addison-Wesley.
  6. Golub, A.P., Klimina, L.A., Lokshin, B.Y. and Selyutskiy, Y.D. (2023), "Autooscillations of a multlink aerodynamic pendulum", J. Comput. Syst. Sci. Int., 62(2), 280-289. https://doi.org/10.1134/S1064230723020089.
  7. Ibrahimbegovic, A., Mejia-Nava, R.A., Hajdo, E. and Limnios, N. (2022), "Instability of (Heterogeneous) Euler beam: deterministic vs. stochastic reduced model approach", Couple. Syst. Mech., 11(2), 167-198. https://doi.org/10.12989/csm.2022.11.2.167.
  8. Kozar, I. and Toric Malic, N. (2014), "Analysis of body sliding along cable", Couple. Syst. Mech., 3(3), 291-304. https://doi.org/10.12989/csm.2014.3.3.291.
  9. Kozar, I., Lozzi Kozar, D. and Toric Malic, N. (2022), "Simple factor analysis of measured data", Couple. Syst. Mech., 11, 33-41. https://doi.org/10.12989/csm.2022.11.1.033.
  10. Mourid, E., Mamouri, S., Kouli, R. and Ibrahimbegovic, A. (2022), "An efficient implicit time stepping scheme for nonlinear dynamics analysis of 3D geometrically exact beam using exponential mapping", Mech. Adv. Mater. Struct., 29(28), 7189-7203. https://doi.org/10.1080/15376494.2021.1994062.
  11. Nguyen, C.U., Hoang, T.V., Hadzalic, E., Dobrilla, S., Matthies, H.G. and Ibrahimbegovic, A. (2022), "Viscoplasticity model stochastic parameter identification: Multi-scale approach and Bayesian inference", Couple. Syst. Mech., 11(5), 411. https://doi.org/10.12989/csm.2022.11.5.411.
  12. Ren, T., Zuo, J., Xu, L., Li, L. and Wang, X. (2024), "An assembly system for inertial pendulum components in miniature wire suspended pendulum accelerometers", J. Mech. Sci. Technol., 1-12. https://doi.org/10.1007/s12206-024-0527-9.
  13. Rukavina, T. and Kozar, I. (2017), "Analysis of two time-delayed sliding pendulums", Eng. Rev., 37, 11-19.
  14. Suljevic, S., Ibrahimbegovic, A., Karavelic, E. and Dolarevic, S. (2022), "Meso-scale based parameter identification for 3D concrete plasticity model", Couple. Syst. Mech., 11(1), 55-78. https://doi.org/10.12989/csm.2022.11.1.055 55.
  15. Wolfram Research Inc. (2022), Mathematica. https://www.wolfram.com/mathematica/.
  16. Zhou, B., Accorsi, M.L. and Leonard, J.W. (2004), "Finite element formulation for modeling sliding cable elements", Comput. Struct., 82, 271- 280. https://doi.org/10.1016/j.ijsolstr.2021.111290.