Free vibration analysis of a circular cylindrical shell using the Rayleigh–Ritz method and comparison of different shell theories

• A systematic procedure is developed to apply the Rayleigh–Ritz method.
• The explicit expressions for the mass and the stiffness matrices are derived.
• The use of beam eigenfuctions as admissible functions is fully discussed.
• Various shell theories are investigated.
• Numerical results are presented.

This study uses the Rayleigh–Ritz method to derive a dynamic model for the free vibration analysis of a circular cylindrical shell. In particular, explicit expressions for the mass and stiffness matrices are obtained to easily implement a computer simulation under different shell theories and boundary conditions. The dynamic model is constructed according to the Donnell–Mushtari theory, which is fully discussed herein, and then, dynamic models are constructed by using Sanders theory, Love–Timoshenko theory, Reissner theory, Flügge theory, and Vlasov theory. This paper also discusses the use of eigenfunctions of a uniform beam as admissible functions that produce compact expressions for the mass and stiffness matrices. The numerical results indicate that the Donnell–Mushtari theory is not sufficiently accurate to calculate the natural frequencies and that there is no discernible difference between the other shell theories considered in this study.