The purpose of this paper is to solve the vibration equations of a ring-stiffened conical shell using the analytical method, and to investigate the vibration characteristics of a ring-stiffened conical shell theoretically.

First, the ring-stiffened conical shell is processed in segments, and its displacement along the radial, circumferential and normal directions is written in the form of power series solutions respectively. The recurrence relations of the coefficients ahead of the power series are then derived in detail. At the same time, a beam model is used to simulate the influence of the number of ring-stiffeners on the vibration characteristics of the conical shell, and the boundary conditions, displacement, internal force matrices and ring-stiffeners of the conical shell segments are assembled and solved, thereby obtaining the vibration response of the shell under harmonic external excitation. Moreover, a comparison of the calculation results with those obtained by the ANSYS finite element analysis is carried out to verify the validity of the proposed method. Finally, the theoretical method is applied to analyze the vibration characteristics of the ring-stiffened conical shell theoretically.

The results show that installing ring-stiffeners on the conical shell can significantly suppress the vibration of the conical shell, which is manifested by the decrease in response amplitude, the increase in natural frequency, and the decrease in the number of resonance peaks within the same frequency band. Increasing the thickness of the shell can reduce the vibration response amplitude and increase the natural frequency of the ring-stiffened conical shell. In addition, increasing the half cone angle, axis length and the number of ring ribs can also reduce the vibration response amplitude of the ring-stiffened conical shell.

The results of this study prove that the method used herein has a certain significance for the theoretical analysis of the vibration characteristics of ring-stiffened conical shells.