Archive of Applied Mechanics

, Volume 88, Issue 12, pp 2231–2246

# Analytical and FEM solutions for free vibration of joined cross-ply laminated thick conical shells using shear deformation theory

• Shahrokh Hosseini-Hashemi
Original

## Abstract

In this study, the free vibration analysis of two joined laminated conical shells is investigated. Five equilibrium equations for each conical shell have been derived in a particular coordinate system; using Hamilton’s principle and first-order shear deformation theorem. The analytical solutions are obtained in the form of power series based on separation of variables method. The boundary conditions at both ends of the joined shells and the continuity conditions, at the conical shells contact, are extracted from energy formulations. As a result, the non-dimensional natural frequencies are studied for cross-ply laminated shells. The effects of semi-vertex angle, circumferential modes, number of layers, thickness, length of shells and different boundary conditions on non-dimensional frequencies are considered. As a comparing result, the non-dimensional frequencies and mode shapes are extracted using finite element method (FEM). The results are compared and verified with the previous available results in other researches. The results reveal a good agreement among analytical solutions, FEM and other results. The output of this paper can be used for analyzing cylindrical–conical shells in addition to joined conical shells.

## Keywords

Free vibration Joined conical shell Laminated shell Shear deformation FEM

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