非保存力学系の動的挙動と不安定現象に関する研究 : (その2) 円形アーチの力オス挙動へのシナリオとフラクタル性

概要

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The submerged shell-like lattice structures with membrane are subjected to follower type as hydrostatic pressure at all times and disturbance forces of various types, existing in a marine environment. These force system may lead the structure to exhibit dynamic instabilities at a much earlier stage than that could be predicted by a static stability criterion. It is necessary to investigate the dynamic behavior of the circular arch that is the basic structural element of shell-like lattice undergoing large deflections and small disturbances. This paper with a characteristic analysis on oscillatory and chaotic behavior of a circular arch subjected to follower forces with small disturbances. The stability region chart of the disturbed equilibrium in an excitation field is calculated numerically. Then, the oscillatory and chaotic behaviors of a circular arch are investigated by executing the time histories of motion, power spectrum, phase plane portraits, Poincare section. By the results of these studies, the dynamic behavior of a circular arch is researched to clarify the scenario from quasi-oscillatory motion to non-periodic motion. Moreover, the correlation dimensions are calculated corresponding to dynamic behaviors of a circular arch. This research can indicate the possibility of making use of the correlation dimension as a stability index.