Vibration analysis of delaminated Timoshenko beams under the motion of a constant amplitude point force traveling with uniform velocity

A composite beam with single delamination traveled by a constant amplitude moving force is modeled accounting for the Poissonʹs effect, shear deformation and rotary inertia. The mechanical behavior between the delaminated surfaces is modeled using a piecewise-linear spring foundation. The governing differential equations of motion for such system are derived. Primarily, eigen-solution technique is used to obtain the natural frequencies and their corresponding mode shapes of such beam. Then, the Ritz method is employed to derive the dynamic response of the beam due to the moving force. The obtained results for the free and forced vibrations of beams are verified against reported similar results in the literatures. Moreover, the maximum dynamic response of such beam is compared with an intact beam. The effects of different parameters such as the force velocity, lamina ply angle, the single delamination size, its span-wise and/or thickness-wise location on the dynamic response of the beam are studied. The effects of delamination parameters on the force critical speed are studied.