BEAM-TYPE MODELING FOR THE FREE-VIBRATION OF A LONG THICK LAMINATED CONICAL TUBE

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.