Natural frequency of laminated orthotropic shells with different boundary conditions and resting on the Pasternak type elastic foundation

Abstract

This paper deals with the vibration analysis of laminated orthotropic shells with different boundary conditions and resting on elastic foundations. Boundary conditions are clamped–clamped ( C– C) and sliding–sliding ( SL– SL). A two-parameter foundation model (Pasternak type) is used to describe the shell–foundation interaction, from which Winkler foundation model can be easily obtained as a limiting case. The modified Donnell type dynamic stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells resting on elastic foundations. Applying Galerkin methods, the natural frequency of the laminated orthotropic truncated conical shell for different boundary conditions, are obtained. The appropriate formulas for laminated cylindrical and complete conical shells are found as special cases. Finally, influences of the elastic foundations, the boundary conditions, the number and stacking sequence, and the variations of shell characteristics on the natural frequency are investigated. The results are compared with their counterparts in the literature.