Vibration characteristics of a stiffened conical shell

Abstract

Abstract This paper is concerned with the free vibrations of a stiffened conical thin shell within the context of Donnell-Mushtari theory. A truncated cone with simply supported ends is reinforced by relatively closely spaced elastic stringers and/or rings. The tapered stringers are used to obtain an efficient stiffening. Change in the stringer spacing in the meridional direction is taken into account in the formulation. The stiffening elements are “smeared out” along the conical shell to yield a single equivalent orthotropic shell. The resulting orthotropic shell has a kind of inhomogeneity due to the tapered stringers. The equations of motion for the free vibrations of the stiffened conical shell are derived by the use of Hamilton's principle. The differential equations of the stiffened truncated conical shell, together with the boundary conditions, are solved by the use of the collocation method. Solutions are presented to show the influence of geometrical parameters and material properties on the vibration characteristics. The numerical results are compared with certain earlier results.