Free vibration of FGM conical–spherical shells: Fid-Bau Portal

Free vibration of FGM conical–spherical shells

Bagheri, H. / Kiani, Y. / Eslami, M.R.

Abstract Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia. The Donnel type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations are discretized using the semi-analytical generalized 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. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells with the data of conventional finite element software, parametric studies are carried out for the system of combined moderately thick conical–spherical joined shells made of FGMs and various types of end supports.

Highlights • Free vibrations of a joined conical–spherical shell system is investigated using the semi-analytical Fourier-GDQ method. • Properties are graded through the thickness where shell is made from a functionally graded material. • Two different types of joined shells are assumed which are the C1-continuous shells and the hemispherical-conical shells. • Minimum frequencies of the joined shell system are associated to he higher circumferential mode numbers.