Theoretical and experimental analysis of the free vibrations of a shell made of n cone segments joined together

This paper investigates the free vibrations of a shell made of n cone segments joined together. The governing equations of the conical shell were obtained by applying the Sanders shell theory and the Hamilton principle. Then, these governing equations are solved by using the power series method and considering a displacement field which is harmonic function about the time and the circumferential coordinate. Using the boundary conditions of the two ends of the shell and the continuity conditions at the interface section of shell segments, and solving the eigenvalue problem, the natural frequencies and the mode shapes are obtained. Very good agreements exist between the analytical results of the present study and the available results in the literature. Also, a shell made of three cone segments is fabricated and experimentally tested. The analytical and experimental results are coincident very well. Finally, some examples are solved in order to study the effects of geometrical parameters as cone angles on modal parameters. Also, as a practical example, natural frequencies of a bell are determined using the formulation presented.