an analytical method for crack detection of beams with uncertain boundary conditions by a concentrated test mass

the aim of this study is to introduce a method for crack detection and simultaneously assessing boundary conditions in beams. this study suggests a method based on the effect of a concentrated test mass on the natural frequency that is defined as a stationary mass, which can be located in different positions of the beam and cannot be separated from the beam. timoshenko beam theory is used to calculate the frequencies. in this method, a beam with the desired number of cracks is modeled. the beam is divided into separated parts at crack section, which are joined together by elastic weightless torsion springs, to avoid non-linearity effects; it is assumed that the crack is always open. at the first step, equations for a cracked beam are extracted by considering the spring boundary conditions. then, to verify the equations, numerical finite element model is used. in this way, a new method is also applied to model the torsion springs in supports and it is shown that suggested model is acceptable. eventually, the obtained responses are evaluated and the sources of errors are identified. to correct the existing errors, a modifying function is suggested. finally, the inverse problem is solved.