Fundamental natural frequencies of thin cylindrical shells: a comparative study

A comparative study of three approximate “explicit” formulae for estimating the fundamental natural frequency of a thin cylindrical shell, and its associated fundamental modenumber is presented. The objective is to identify the limits of the validity of each formula. The three approximate formulae considered in this study are based on: (a) the Weingarten–Soedel approximation of the Donnell–Mushtari–Vlasov equations, (b) the Calladine–Koga improved classical-beam-on-Winkler-foundation model, and (c) the Timoshenko-beam-on-Pasternak-foundation analogy of the shell. Results are compared against the analytical solutions of the equations of motion of Flügge, and results obtained by a commercial finite-element package. Tabulated results are given for length-to-radius ratios of 1, 2, 5, 10, and 20, and radius-to-thickness ratios of 20, 50, 100, 200, and 500.