Forced vibration analysis of a Timoshenko cracked beam using a continuous model for the crack

In this paper, forced flexural vibration of a cracked beam is studied by using a continuous bilinear model for the displacement field. The effects of shear deformation and rotary inertia are considered in the model. The governing equation of motion for the beam is obtained using the Hamilton principle and based on the proposed displacement field. The equation of motion is given for a general force distribution. Then, the equation of motion has been solved for a concentrated force to present a numerical simulation of the method. The frequency response diagrams obtained from this study are compared with the finite element results to demonstrate the accuracy of the method. The results are also compared to results of a similar model with Euler-Bernoulli assumptions to confirm the advantages of the proposed model in the case of short beams.