Free vibrational characteristics of isotropic coupled cylindrical–conical shells

This paper presents the free vibrational characteristics of isotropic coupled conical–cylindrical shells. The equations of motion for the cylindrical and conical shells are solved using two different methods. A wave solution is used to describe the displacements of the cylindrical shell, while the displacements of the conical sections are solved using a power series solution. Both Donnell–Mushtari and Flügge equations of motion are used and the limitations associated with each thin shell theory are discussed. Natural frequencies are presented for different boundary conditions. The effect of the boundary conditions and the influence of the semi-vertex cone angle are described. The results from the theoretical model presented here are compared with those obtained by previous researchers and from a finite element model.