ABSTRACT
An analysis of large amplitude free vibrations of clamped rotationally symmetric spherical shells of variable thickness using displacement formulations has been presented. The normal component of the displacement of the middle surface of the shell is considered to be positive from the concave to the convex direction. The radial displacement of a point in the middle surface is measured meridionally away from the axis of symmetry. First, the differential equation for the in-plane displacement has been solved. The final equation for the time function is obtained by Galerkin’s technique which is solved to find the linear and nonlinear frequencies. Numerical values for the nonlinear to linear frequency ratio have been calculated both for movable as well as immovable edges. These are shown graphically and compared to other known results.
