Free vibration analysis of joined conical shells: Analytical and experimental study

• We presented natural frequencies and mode shapes of two joined conical shells.
• Governing equations are obtained using Donnell shell and Hamilton׳s principle.
• Results are compared and validated with other investigations and modal testing.
• Effects of some geometrical properties on the natural frequency are presented.

Natural frequencies and mode shapes of two joined isotropic conical shells are presented in this study. The joined conical shells can be considered as the general case for joined cylindrical–conical shells, joined cylinder–plates or cone–plates, conical and cylindrical shells with stepped thicknesses and also annular plates. Governing equations are obtained using thin-walled shallow shell theory of Donnell and Hamilton׳s principle. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved assuming trigonometric response in circumferential and series solution in meridional directions and all combinations of boundary conditions can be assumed in this method. The results are compared and validated with the available results in other investigations and also modal testing. The effects of semi-vertex angles and meridional lengths on the natural frequency and circumferential wave number of joined shells are investigated.