擾乱による構造の非周期運動と相関次元 - 従動力を受ける円形アーチのカオス挙動-

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. The dynamic behavior of a circular arch, as basic structural element of shell-like lattice, should be investigated the complicated phenomenon undergoing large deflections with small disturbances. This paper deals with the correlation dimensions corresponding to dynamic behaviors of a circular arch subjected to follower forces with small disturbances. For that purpose, the finite deformation and dynamic behavior of a circular arch are numerically analyzed in a mono-clinically particle coordinates description. Then, the oscillatory and chaotic behaviors of a circular arch are investigated by executing the power spectrum, phase plane portraits and Poincare section. Moreover, the correlation dimensions are calculated corresponding to dynamic behaviors of a circular arch. This research can be clarified that the correlation dimensions related to dynamic behaviors may give a sign of changing from quasi-oscillatory motion to non-periodic motion and this fact can indicate the possibility of making use of the correlation dimension as a stability index.