Free vibration analysis of axially loaded cracked Timoshenko beam structures using the dynamic stiffness method

In this article, the purpose is to investigate the changes in the magnitude of natural frequencies and modal response introduced by the presence of a crack on an axially loaded uniform Timoshenko beam using a particular member theory. A new and convenient procedure based on the coupling of dynamic stiffness matrix and line-spring element is introduced to model the cracked beam. The application of the theory is demonstrated by two illustrative examples of bending–torsion coupled beams with different end conditions, for which the influence of axial force, shear deformation and rotatory inertia on the natural frequencies is studied. Moreover, a parametric study to investigate the effect of the crack on the modal characteristics of the beam is conducted.