Free vibration of joined conical-conical shells

Abstract

Free vibration analysis of a joined shell system composed of two conical shells is analysed in this research. It is assumed that the system of joined shell is made from a linearly elastic isotropic homogeneous material. Both shells are unified in thickness. To capture the through-the-thickness shear deformations and rotary inertias, first order theory of shells is accompanied with the Donnell type of kinematic assumptions to establish the general motion equations and the associated boundary and continuity conditions with the aid of Hamilton's principle. The resulted system of equations are discreted using the semi-analytical generalised differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies as well as the associated mode shapes. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick conical-conical.