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Sub-harmonic vibration of clamped-free thin cylindrical shells immersed in fluid under seismic excitation was investigated by numerical simulation. The conditions when the sub-harmonic vibration occurs under narrow-band random waves were compared with those under sisusoidal wave excitations : the critical pressures under narrow-band random waves were higher than those under sinusoidal waves. It was also found that the frequency componets other than the dominant frequency of a narrow-band random wave have a negligible effect on the occurrence of the sub-harmonic vibration. These two findings provide the basis for a simple equation for predicting the critical pressure under narrow-band random waves.

An upright stainless steel circular cylinder with a mass attached at midlength is excited seismically in the horizontal direction using a vibration table. A well-known seismic wave called EI Centro 1940 NS is applied to excite the test specimen. Fourier components over 10Hz of the seismic wave are cut off and the duration is shortened to 30%, 40%, or 50%. The eccentricity of the center of gravity of the attached mass is varied and the amplitude of the modified El Centro 1940 NS is increased incrementally. Parametric excitation is observed for each combination of eccentricity of the attached mass and time scale of the seismic wave.

The displacement functions of an axisymmetric shell with eccentrically attached masses are expanded using the free vibration modes of the axisymmetric shells without attached masses. These base vectors for expansion are calculated using a conical shell finite element. The expanded functions are used to express the strain energy and kinetic energy. The contribution of the rocking motion of the attached masses to the kinetic energy is considered. Also the effects of contained liquid are included. The strain energy and kinetic energy are substituted into Lagrange's equations to obtain natural frequencies, vibration modes and response for base excitation. Analytical results using the present method show good agreement with analytical results obtained by other methods or experimental results.

The parametric resonance of an axisymmetric shell-lumped weight system subjected to periodic acceleration in the radial direction is analyzed. Symmetric and asymmetric free-vibration modes of the system are derived using the free-vibration modes of the axisymmetric shell without lumped weight. The aforementioned eigenmodes are calculated by employing a conical shell finite element. Modal Mathieu equations of the system are derived, and the parametric resonance regions of the system are calculated using Bolotin's method, considering the effect of translational motion of the lumped weight in the radial direction. Also, a circular cylindrical shell with a lumped weight is experimentally investigated using a vibration table. Numerical results of the parametric resonance regions of the system show good agreement with experimental results.

Free vibration and buckling of axisymmetric shells, with thickness which are changed locally, are analyzed. the displacement functions of these shlls are expanded using the free vibration modes of the axisymmetric shells with constant thickness around the circumference. These basis vectors for expansion are calculated using a conical shell finite-element. The expanded functions are used to express the strain energy and kinetic energy. the eigenvalue equations are derived by substituting the strain energy and kinetic energy into Lagrange's equations. Analytical results using the present method show good agreement with analytical results obtained by other methods or experimental results.

An approximate method is proposed for the analysis of liquid containers considering the effects of the compressibility of the liquid. This method is based on the expansion of the vibration mode of compressible fluid-structure interaction using the coupled modes of incompressible fluid-structure system. Further simplified equations are derived assuming that the vibration modes are not changed when fluid compressibility is included. This paper also shows a technique to avoid the drawback of the mass matrix becoming the full matrix when fluid-structure interaction is considered. It consists of solving simultaneous equations utilizing the sparsity of fluid stiffness matrix without composing the full matrix in the subspace interation method for eigenvalues. Calculated natural frequencies and frequency response spectra, including compressibility of fluid, agree well with experimental results.