Objectives The purpose of this paper is to study the free vibration characteristics of cylindrical shell with T-section rings and bulkheads under different boundary conditions based on Rayleigh−Ritz method.

Methods The classical Love shell and thin plate theory are used to establish the mathematical and physical model of cylindrical shell and bulkheads. Using the Euler−Bernoulli beam theory, the T-shaped ring rib is regarded as a discrete element, and the mathematical model is established by coordinate transformation through the relationship between its cross-section centroid and the displacement angle of the mid-surface of the shell. Modified Fourier series are selected as displacement penalty functions to integrate displacement expression of cylinder, plate and T-section rings. The penalty function is introduced to change the spring stiffness to simulate the continuous conditions between bulkhead shells and the boundary conditions at both ends. The governing equations for the vibration of the coupled structure are obtained by means of energy functions.

Results By comparing with the results of the numerical method, the convergence, accuracy and reliability of the proposed method are verified.

Conclusion The results show that the number and position of the T-section rings and bulkheads are closely related to the natural vibration characteristics of the coupled structure, providing certain reference for engineering designs and applications.