By using a C-0 continuous, QUAD-4 shear flexible shell element, based
on the field consistency principle, the non-linear free flexural vibra
tions of thin circular cylindrical shells have been studied. The formu
lation is general in the sense that it includes anisotropy, transverse
shear deformation, in-plane and rotary inertia effects. Primarily, an
attempt is made to clarify the existing controversies in the predicti
on of the non-linear behaviour of isotropic circular cylindrical shell
s through a finite element formulation with dynamic response analysis.
The non-linear governing equations are solved by using a Wilson-theta
numerical integration scheme with theta = 1.4. For each time step, mo
dified Newton-Raphson iterations are employed to achieve equilibrium a
t the end of that time step. Detailed numerical results are presented
for various parameters for the isotropic shell. The present study also
brings out the participation of the axisymmetric contraction mode wit
h the asymmetric mode. (C) 1996 Academic Press Limited