An Analytical Method of Calculating Natural Frequency of Cylindrical Shell Containing Strong Intermediate Support Boundary

摘要

An analytical method of calculating natural frequency of ring-stiffened cylindrical shell with arbitrary boundary conditions and arbitrary layout of rings is presented. According to Donnel theory, the general solution to governing equations of cylindrical shell is given. The stiffened rings, which can be either even spaced or uneven spaced, are treated as discrete members. The rings are modeled as beams, with the flexural, extensional, and torsional motion considered as well as the in-plane inertia terms. The cylindrical shell is divided into several parts according to the positions of rings, and each part is supported by two inter-rings at both ends. According to continuity of displacements and forces between each bay of cylindrical shell and inter-rings, an equation about eight unknown constant coefficients are obtained. Combined with the boundary conditions of the whole cylindrical shell at both ends, the equation can be assembled in a matrix form. With the determinant of the matrix to be zero, natural frequency of cylindrical shell can be solved. Numerical results show that the methods presented in this paper have a good agreement with that calculated by Finite Element Method (FEM). Furthermore, natural frequency of cylindrical shell containing intermediate strong support is calculated. The results show that, modes which can be recognized as "cabin subdivision effect " arise from the existence of intermediate strong support.