Flexural–torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM

This study introduces the differential transform method (DTM) to analyse the free vibration response of an axially loaded, closed-section composite Timoshenko beam which features material coupling between flapwise bending and torsional vibrations due to ply orientation. The governing differential equations of motion are derived using Hamiltonʹs principle and solved by applying DTM. The mode shapes are plotted, the natural frequencies are calculated and the effects of the bending–torsion coupling, the axial force and the slenderness ratio on the natural frequencies are investigated using the computer package, Mathematica. Wherever possible, comparisons are made with the studies in open literature.