Steel and Composite Structures

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Non-periodic motions and fractals of a circular arch under follower forces with small disturbances

  • Received : 2004.11.02
  • Accepted : 2005.10.17
  • Published : 2006.04.25
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Abstract

The deformation and dynamic behavior mechanism of submerged shell-like lattice structures with membranes are in principle of a non-conservative nature as circulatory system under hydrostatic pressure and disturbance forces of various types, existing in a marine environment. This paper deals with a characteristic analysis on quasi-periodic and chaotic behavior of a circular arch under follower forces with small disturbances. The stability region chart of the disturbed equilibrium in an excitation field was calculated numerically. Then, the periodic and chaotic behaviors of a circular arch were investigated by executing the time histories of motion, power spectrum, phase plane portraits and the Poincare section. According to the results of these studies, the state of a dynamic aspect scenario of a circular arch could be shifted from one of quasi-oscillatory motion to one of chaotic motion. Moreover, the correlation dimension of fractal dynamics was calculated corresponding to stochastic behaviors of a circular arch. This research indicates the possibility of making use of the correlation dimension as a stability index.

Keywords

References

  1. Buskirk, R. V. and Jeffries, C. (1985), 'Observation of chaotic dynamics of coupled nonlinear oscillations', Physics Review; A31, 3332-3357
  2. Fukuchi, N., Tanaka, T. and Okada, K. (2000), 'A characteristic analysis on dynamic stability of shell-like lattice structures subjected to follower forces', Advances in Computational Engineering and Sciences; 2, 1816-1821
  3. George, T. and Fukuchi, N. (1993), 'Dynamic instability analysis of thin shell structures subjected to follower forces, (4th Report) quantitative stability of disturbed', J. of the Society of Naval Architects of Japan; 174, 787-796
  4. George, T. and Fukuchi, N. (1994), 'Dynamic instability analysis of thin shell structures subjected to follower forces, (5th Report) disturbance threshold curves of dynamic stability', J. of the Society of Naval Architects of Japan; 175, 337-348
  5. Jackson, E. A. (1991), Perspectives of Nonlinear Dynamics I, Cambridge University Press
  6. Judd, K. (1992), 'An improved estimator of dimension and some comments on providing confidence intervals', Physica; D56, 216-228
  7. Libchaber, A. and Maurer, J. (1982), 'A Rayleigh benard experiment: Helium in a small box', Nonlinear Phenomena at Phase Transitions and Instabilities; 259-286
  8. Martin, S., Leber, H. and Martinsen, W. (1984), 'Oscillatory and chaotic states of the electrical conduction in barium sodium niobate crystals', Physics Review; Lett. 53, 303-306 https://doi.org/10.1103/PhysRevLett.53.303
  9. Moon, F. C. (1987), Chaotic Vibrations, John Wiley and Sons
  10. Moon, F. C. (1992), Chaotic and Fractal Dynamics, John Wiley and Son
  11. Thompson, J. M. T. and Stewart, H. B. (1986), Nonlinear Dynamics and Chaos, John Wiley and Sons

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