Study Regarding the Effect of Crack Branching on the Eigenfrequencies of Beams Cristian Tufisi , Gilbert-Rainer Gillich (&) , Codruta Oana Hamat , and Tiberiu Manescu Department of Mechanical Engineering, Universitatea “Eftimie Murgu” din Resita, P-ta Traian Vuia 1-4, 320085 Resita, Romania gr.gillich@uem.ro Abstract. The paper presents a study regarding the vibration behavior of Euler- Bernoulli beams which have cracks with complex shapes. The aim is to show that diverse orientations of the crack branches occurring in a given region of the structure produce different changes of the eigenfrequencies for the different vibration modes, dependent on the position and propagation angle of the crack. The research is conducted employing the finite element analyses, which are used to describe the dynamic response of a structure affected by a transversal open crack followed by two branches, each oriented at a different angle. These cracks are traditionally referred to as Y-shaped crack. We calculated the relative fre- quency shifts for the first six transverse vibration modes and extracted the damage signature for the considered branched crack location. The damage signatures can be used as patterns in damage detection procedures, transforming the procedure of detecting the crack position and severity from the eigenfre- quency changes in an inverse problem. Keywords: Damage detection  Beam-like structure  Branched crack  Damage signature  Frequency shift 1 Introduction Damages reduce the capacity of the beams to store energy because the slices where damage is present are subject to stiffness decrease. As a consequence, the eigenfre- quencies of damaged beams decrease [1–4]. The frequency decrease depends on the reduction of the cross-sectional area, hence on the crack depth, but also on the crack position [5–7]. For transverse cracks, either open or breathing, mathematical relations which permit predicting the frequency drop if the crack depth and position are known to exist and are widely presented in the literature [8–11]. Most mathematical relations were derived empirically, from the fracture mechanics theory, and are applicable just for particular cases [12, 13]. Our research has been focused on finding a mathematical relationship with a large degree of generality, and we have succeeded in creating a relationship that can be applied to any beam-like structure if it is subject to a transverse crack [14–16]. Our recent research is focused on cracks with Y-shaped branches [17], which have increased complexity and therefore more parameters that influence the frequency © Springer Nature Singapore Pte Ltd. 2020 M. A. Wahab (Ed.): DAMAS 2019, LNME, pp. 79–91, 2020. https://doi.org/10.1007/978-981-13-8331-1_6