Vibrations of polar orthotropic laminated shallow spherical shells by Godunov method

Abstract

The present study deals with free vibrations of laminated shallow spherical shells composed of linearly elastic orthotropic layers with constant thickness. The principal material directions are assumed to coincide with the shell curvature directions. Hamilton's variational principle is used to obtain the dynamic governing equat,ions in terms of displacements for both first order shear deformation (SH) and the classical-type KirchhoffLove (CL) theories. Five Mindlin-type displacement variables are utilized to take into account a thickness shear. A tenthand eighth-order systems of linear partial differential equations are obtained for SHand CL-cases, respectively. The equations obtained are transformed then into matrix form including only first order derivatives of new unknown functions which enables to apply the Godunov method. High-strength graphite-epoxy (EISG) 3-layer cross-ply laminatcd shallow spherical cap is chosen for parametric studies. The transverse shear and rotational inertia effects are discussed here.