The Application of the Mathematical Modeling of FGM Beams in the Non-Destructive Detection of the Point Damage of Homogeneous Beams

Non-destructive testing of already existing structures is one of the most challenging tasks of modern engineering. In this article a homogeneous beam with a certain small, arbitrarily localized damaged section is considered. A ’damaged section’ should be understood as a certain small part of a beam, which has significantly lower elastic modulus than the rest of the structure. This small part is modeled as a specific case of functionally graded material (FGM). Based on analysis of its axial vibrations, a relation between reduced elastic modulus and a velocity of the short traveling wave is obtained. Consequently, a procedure of non-destructive testing of homogeneous beams is presented, which allows us to assess not only the position and dimension of the ’damaged’ part, but also to estimate a reduction ratio of the elastic modulus. The proposed procedure is validated in the paper by the comparison of its results with the finite element method calculations. As a consequence, its applicability limits are defined, as relative errors between results can vary (0–26%), depending on the calculation case. Such a procedure can have multiple applications in modern engineering.