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Helicoseir as Shape of a Rotating String (II): 3D Theory and Simulation Using ANCF

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Abstract

This paper is the second one devoted to studying the dynamical behavior of a rotating uniform string with one fixed top point. Two-dimensional shapes of relative equilibrium for a string were analyzed in our paper [3] both analytically and numerically and found to be instable. This fact disagrees with the experimental appearance of this so-called helicoseir problem because one can easily demonstrate that its stable motion is possible. In this paper, spatial nonlinear equations of motion are derived and shown that a 2D equilibrium equation is one of their partial cases. The equations are, however, very complicated that is why we decided at first to analyze the motion numerically by a finite element approach called the absolute nodal coordinate formulation (ANCF). We developed a new 12-dof element of a thin string based on the Euler-Bernoulli theory. The simulation shows that the undamped spatial motion of the helicoseir is stable and looks like self-excited oscillations near the flat instable configurations that were obtained previously. This stability is destroyed when external damping is added to the system. Some examples of bifurcation instability fore spatial motion are presented; they satisfy the bifurcation diagram obtained in the previous work. Unfortunately, numerical simulation cannot give answers to some interesting questions, e.g. dependence of parameters of the self-excited oscillations on the angular velocity of rotation. Thus, further analytical research of this problem is desirable.

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Authors and Affiliations

  1. National Research Laboratory of CAE, Pusan National University, Busan, Korea

    Oleg Dmitrochenko (Post-doctoral Researcher)

  2. Director of National Research Laboratory of CAE, Pusan National University, Busan, Korea

    Wan-Suk Yoo (Professor)

  3. Department of Applied Mechanics, Bryansk State Technical University, Bryansk, Russia

    Dmitry Pogorelov (Professor)

Authors
  1. Oleg Dmitrochenko
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  2. Wan-Suk Yoo
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  3. Dmitry Pogorelov
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Correspondence to Oleg Dmitrochenko.

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Dmitrochenko, O., Yoo, WS. & Pogorelov, D. Helicoseir as Shape of a Rotating String (II): 3D Theory and Simulation Using ANCF. Multibody Syst Dyn 15, 181–200 (2006). https://doi.org/10.1007/s11044-005-9004-0

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  • DOI: https://doi.org/10.1007/s11044-005-9004-0

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