Free Vibration of Delaminated Composite Shallow Conical Shells

Abstract

This paper presents a finite element method to investigate the effects of delamination on free vibration characteristics of graphite-epoxy pretwisted shallow angle-ply composite conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The theoretical formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. 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 standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain numerical results concerning the effect of twist angle, location of delamination and rotational speed on natural frequencies of delaminated angle-ply composite conical shells. The mode shapes are also depicted for a typical laminate configuration. Parametric studies of symmetric and anti-symmetric angle-ply laminates provide the non-dimensional natural frequencies which are the first known results for the type of analyses carried out here.