Free vibration analysis of rotating thin-walled composite beams

In this paper, both analytical and finite element formulations of a rotating thin-walled composite beam are derived for the flapwise bending, chordwise bending and torsional displacements. In the analytical part, derivation of both strain and kinetic energy expressions are made and the equations of motion are obtained by applying the Hamilton´s principle. The equations of motion are solved by applying the Differential Transform Method (DTM). In the finite element part, structural matrices are obtained by using the derived energy expressions and a finite element code is written to calculate the natural frequencies. The analysis is carried out for anti-symmetric lay-up configuration also referred as Circumferentially Uniform Stiffness (CUS). Effect of the ply orientation on the natural frequencies is investigated. The natural frequencies are validated by making comparisons with the results in literature. Consequently, it is observed that there is a good agreement between the results.