A procedure for analyzing parametric resonance of liquid storage axisymmetric shells is proposed that is an extension of the procedure presented at PVP-89 for parametric resonance of empty axisymmetric shells with lumped weights. Free vibration modes of axisymmetric shells containing liquid are calculated considering the effect of initial stress due to static liquid pressure by using a conical shell finite element. The calculated free vibration modes are used to expand the free vibration modes of the axisymmetric shell with lumped weights and internal liquid. A type of Mathieu equation is derived considering the effects of the translational motion of the attached weight in the radial direction or the effects of the beam-type motion of the shell without lumped weight. The harmonic balance method is used to obtain the parametric resonance regions. Principal resonance of a circular cylindrical shell with an attached weight and combination resonance of a liquid storage circular cylindrical shell without attached weights are analyzed. Analytical results show good agreement with experimental results.

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