A dynamic stiffness method is presented for determining the free vibration
frequencies and mode shapes of thick spherical shell segments with variable thickness
and different boundary conditions. The analysis uses the equations of the
two-dimensional theory of elasticity, in which the effects of both transverse shear
stresses and rotary inertia are accounted for. The displacement components are taken
to be sinusoidal in time, periodic in the circumferential direction, constant through
the thickness, and solved exactly in the meridional direction using the exact
element method. The shape functions are derived from the exact solutions for
the system of the differential equation of motion with variable coefficients.
The dynamic stiffness matrix is derived from the exact shape functions and
their derivatives. High-precision numerical results are presented for thick
spherical shell segments with constant or linearly varying thickness and for
several combinations of boundary conditions. Comparison is made with results
of published research and with two- and three-dimensional finite element
analyses.
