Free vibration analysis of delaminated composite pretwisted rotating shells - A finite element approach

In this paper a finite element method is presented to study the effects of delamination on free vibration characteristics of graphite-epoxy composite pretwisted rotating shells. Lagrange's equation of motion is used to derive the dynamic equilibrium equation and moderate rotational speeds are considered wherein the Coriolis effect is negligible. An eight noded isoparametric plate bending element is employed in the formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin's theory. To satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front, a multipoint constraint algorithm is incorporated which leads to unsymmetric stiffness matrices. Parametric studies are performed in respect of location of delamination, fibre orientation, rotational speed and twist angle on natural frequencies of cylindrical shallow shells. Numerical results obtained for symmetric and unsymmetric laminates are the first known non-dimensional frequencies for the analyses carried out here.