Explicit Frequency Response Function of beams with Crack of Uncertain Depth

Detection of cracks in structural components and identification of their size for structures having beam form is of crucial importance in many engineering applications. Usually, the crack characteristics are assumed to be known. However they possess considerable scatter or uncertainty assumed in this paper by both a probabilistic and non-probabilistic model. In order to evaluate the main statistics as well the upper and lower bounds of the response, the Frequency Response Function of damaged beams with uncertain depth of the crack is derived in explicit approximate form.