This paper presents a finite element method to investigate the effects of multiple
delaminations on the free-vibration characteristics of graphite-epoxy bending-stiff
composite pretwisted shallow conical shells. (We call
bending-stiff a laminate
configuration having maximum stiffness for the spanwise first bending mode.) The
generalized dynamic equilibrium equation is derived from Lagrange’s equation of
motion neglecting the Coriolis effect for moderate rotational speeds. An
eight-noded isoparametric plate bending element is employed in the finite element
formulation incorporating rotary inertia and the effects of transverse shear
deformation based on Mindlin theory. A multipoint constraint algorithm
is utilized to ensure the compatibility of deformation and equilibrium of
resultant forces and moments at the delamination crack front. The standard
eigenvalue problem is solved by applying the QR iteration algorithm. Finite
element codes are developed to obtain numerical results concerning the effects
of twist angle and rotational speed on the natural frequencies of multiple
delaminated bending-stiff composite conical shells. The mode shapes are also
depicted for a typical laminate configuration. The numerical results obtained
for comparison of single and multiple delaminated bending-stiff composite
laminates are the first known nondimensional natural frequencies under the
combined effect of rotation and twist for the type of analyses carried out
here.
