Free vibration analysis of joined cross-ply laminated conical shells

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

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