On the Accurate Analysis of Free Vibration of Open Circular Cylindrical Shells

This paper considers the analytical methods used and the boundary conditions encountered in the accurate free vibration analysis of open circular cylindrical shells. The simple boundary conditions associated with the Donnell-Mushtari theory of thin shells are classified into primary and secondary boundary conditions. Different combinations of these primary and secondary boundary conditions lead to the use of different analytical methods. Exact solutions for basic shells with different combinations of primary boundary conditions are obtained using the generalized Navier method. Accurate solutions for shells with secondary and mixed boundary conditions are obtained by using the method of superposition. One needs to investigate only four primary and nine secondary basic shells in order to obtain solutions for shells with arbitrary combinations of simple boundary conditions.