Techno Press

Steel and Composite Structures   Volume 6, Number 2, April 2006, pages 87-101
Non-periodic motions and fractals of a circular arch rnunder follower forces with small disturbances
Nobuyoshi Fukuchi and Takashi Tanaka

Abstract     [Full Text]
    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.
Key Words
    dynamic stability; non-conservative nature; circular arch; follower force; instability region; correlation dimension; chaotic behaviors.
Nobuyoshi Fukuchi; Graduate School of Engineering, Kyushu University, 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812-8185, JapanrnTakashi Tanaka; Japan Marine Science Inc., 2-3-6 Minami-Shinagawa, Shinagawa-ku, Tokyo 140-0004, Japan

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