Dc. Winfield et al., BEAM-TYPE MODELING FOR THE FREE-VIBRATION OF A LONG THICK LAMINATED CONICAL TUBE, Composites. Part B, Engineering, 28(5-6), 1997, pp. 555-563
The free vibration of a long thick laminated conical tube is studied i
n this paper with a beam-type model. Taken as a beam, the tube is divi
ded into elements by cross-sections. Each cross-section is a node. in
the beam type model, the nodal forces are assumed to be uniformly dist
ributed along the middle circle, which is the intersection of the cros
s-section with the middle surface of the tube. The nodal torsional mom
ent is assumed to be produced by a uniformly distributed tangential fo
rce along the middle circle. The nodal bending moments are assumed to
be produced by sinusoidally distributed axial forces along the middle
circle. Three nodal displacements and three nodal rotations correspond
ing to these nodal forces and moments, respectively, are determined by
the energy principle and the assumed deformation pattern. Thus, in th
e beam-type model, there are only six degrees of freedom at each node.
The stiffness matrix in terms of these nodal degrees of freedom is de
rived from a thick-shell theory together with a semi-analytical method
. Based on the stiffness matrix, the frequencies of free vibration are
calculated. The numerical results are checked bq experimental measure
ments with good agreement. (C) 1997 Elsevier Science Limited.