Study of Phenomena of Jump and Chaos in a Non-linear Beam with Concentrated Mass Under the Effects of Water Flow

Document Type : Dynamics, Vibrations, and Control

Authors

1 MSc, Faculty of Engineering, Imam Hossein University, Tehran, Iran

2 Corresponding author: Associate Professor, Faculty of Engineering, Imam Hossein University, Tehran, Iran

3 MSc, Faculty of Engineering, University of Tabriz, Tabriz, Iran

Abstract

In the analysis of many offshore structures such as oil columns and structures, oil rig abutments and towers surrounded by water, the single-beam model is usually used. These models usually bear the weight of a concentrated mass, and the response amplitude of these structures is of particular importance during design.
In this paper, a nonlinear beam immersed in a fluid with a concentrated mass under the effects of the harmonic flow of water has been studied. Using the harmonic balancing method, the response of a nonlinear beam with three nonlinear terms is determined in the first four modes. Examination of the frequency response by analytical solution and numerical simulation shows that the jump phenomenon occurs in the triple response zone between the bifurcation points. The jump phenomenon is hardening in the first mode and softening in the second to fourth modes. Each of the nonlinear sentences has different effects on the vibrational behavior of the system and the jump phenomenon. The behavior of the beam in the state space along with the time response and Poincaré mapping shows that the path of the phase curve has different stability points. Finally, the phenomenon of chaos in the nonlinear beam was studied. At the bifurcation points, the behavior of the system is chaos, and the geometric nonlinear sentence has the most effective effect on the response disorder.

Keywords

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References

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Aerospace Mechanics
Volume 18, Issue 2 - Serial Number 68
Serial No. 68, Summer Quarterly
August 2022
Pages 157-167

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History

  • Receive Date: 06 January 2022
  • Revise Date: 27 February 2022
  • Accept Date: 28 February 2022
  • Publish Date: 23 July 2022

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