Torsional vibrations of composite bars of variable cross-section by BEM

In this paper a boundary element method is developed for the nonuniform torsional vibration problem of doubly symmetric composite bars of arbitrary variable cross-section. The composite bar consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli and are firmly bonded together. The beam is subjected to an arbitrarily distributed dynamic twisting moment, while its edges are restrained by the most general linear torsional boundary conditions. A distributed mass model system is employed which leads to the formulation of three boundary value problems with respect to the variable along the beam angle of twist and to the primary and secondary warping functions. These problems are solved employing a pure BEM approach that is only boundary discretization is used. Both free and forced torsional vibrations are considered and numerical examples are presented to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. The discrepancy in the analysis of a thin-walled cross-section composite beam employing the BEM after calculating the torsion and warping constants adopting the thin tube theory demonstrates the importance of the proposed procedure even in thin-walled beams, since it approximates better the torsion and warping constants and takes also into account the warping of the walls of the cross-section.