Moving load-induced response of damaged beam and its application in damage localization

The dynamic response of a beam under a moving load is a superposition of two components, namely, the moving-frequency component corresponding to the moving load and the natural-frequency component of the beam. This study investigates the closed-form solution of the dynamic response of a damaged simply supported beam subjected to a moving load and examines the effects of the loss of local stiffness on these two components. The study provides deep insights into beam damage detection based on moving load-induced response. Consequently, a simple and intuitive method for damage localization is developed. First, the closed-form solution is derived based on the modal perturbation and modal superposition method. The closed-form solution enables the individual examination of damage-induced changes in moving- and natural-frequency components. The results show that the moving-frequency component is preferred in damage localization. Then, multi-scale discrete wavelet transform is employed to separate the moving-frequency component from the total dynamic response and to subsequently locate the damage. Numerical examples with single or multiple damages are utilized to validate the efficacy of the proposed response computation algorithm and to demonstrate the effectiveness of the corresponding damage localization method. The effects of moving velocity and noise level are carefully studied. In particular, the effects of varying moving velocities and moving vehicular dynamics on damage localization are presented in this paper.