On the response spectra of cracked beams under different types of moving force

In this paper, the dynamic responses of cracked beams under different moving forces, including moving load, moving mass, moving oscillator, and four-degrees-of-freedom moving system, are investigated. Structural elements such as beams are designed to withstand the predicted loads, but unfortunately, they are always exposed to unpredictable damage such as cracks. Several factors may cause these damages, and the important thing is that their presence can affect the dynamic behavior of the beam or even endanger its reliability and durability in some cases. Therefore, this study considers an Euler-Bernoulli single-span beam with simple supports and a crack. First, with the help of the function expansion method and by employing MATLAB software, the dynamic time history responses of the beam at its midpoint under the influence of each type of moving force are extracted. Then, the changes in maximum displacement responses due to various parameters such as velocity, load magnitude, crack depth, and crack location are plotted in different spectra and compared with each other. The results show that the beam will have close results under all types of moving force (moving load, moving oscillator, and moving system) except moving mass. Obviously, this difference is due to the effect of inertia on the moving mass.