Crack localisation and sizing in a beam based on the free and forced response measurements

In the present paper, a method of the crack localisation and sizing in a beam from the free and forced response measurements is developed. The method gives crack flexibility coefficients as a by-product. Timoshenko beam theory is used in the beam modelling for transverse vibrations. The finite element method (FEM) is used for the cracked beam free and forced vibration analysis. An open transverse surface crack is considered for the crack model. The effect of the proportionate damping has been included. A harmonic imbalance force of known amplitude and frequency is used to dynamically excite the beam with the help of an independent exiting unit. The crack localisation and sizing algorithm is iterative in nature. The iteration starts with an initial guess for the crack depth ratio and iteratively estimates the crack location and the crack depth until getting the desired convergence for both the crack location and the crack depth. For estimation of bounded flexibility coefficients, a regularisation technique has been adopted. The method has been illustrated through numerical examples. The prediction of the crack location and size are in good agreement even in the presence of the measurement error and noise.