Natural frequencies of delaminated composite rotating conical shells—A finite element approach

Abstract

This paper presents the effect of rotational speeds on free vibration characteristics of delaminated twisted graphite–epoxy cross-ply composite conical shells employing finite element method. Theoretical formulation is based on Mindlin's theory considering an eight noded isoparametric plate bending element. A generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting the Coriolis effect for moderate rotational speeds. The multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The QR iteration algorithm is used for solution of standard eigenvalue problem. Finite element codes are developed to obtain the numerical results concerning the combined effects of twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes for a typical laminate configuration are also depicted. Numerical results obtained for cross-ply laminates with delamination are the first known non-dimensional frequencies for the type of analyses carried out here.