Abstract
It is the purpose of this report to formulate and solve theoretically the rocking motions of cantilevered circular cylindrical shells partially filled with liquid subjected horizontal earthquake excitations. For containers, thin cylindrical shells are considered and a rigid rotation about a horizontal axis perpendicular to the plane of vibration is considered under the rigid base and the internal liquid is assumed to be ideal liquid. The stiffness of the foundation under the base is assumed to be independent to the excitation frequencies. The fundamental equations are obtained based on the Flugge approximation, the linear elastic shell theory with small deflection and the potential flow theory. Since the frequencies of the first few dominant modes of liquid sloshing are usually much smaller than the frequencies of liquid-shell system, the impulsive pressure is derived by an assumption of rigid motion with respect to the free surface of internal liquid. The impulsive pressure is devided into the pressures of rocking mode, elastic displacement mode and rigid motion mode, respectively. The method used herein are that the unit displacement modes are expanded into the series based on the Rayleigh-Ritz method and boundary value problems on the shell surface are solved with respect to the three displacement mode of the shell. Numerical computations proved that the rocking mode is dominant mode at the first natural mode and decrease the natural frequencies of fixed shells and increase the response pressures of tall shells.
