Crack Detection in Stepped Beam Carrying Slowly Moving Mass

Abstract

A crack identification algorithm based on a mathematical model has been developed to identify crack location and depth in stepped cantilever Euler—Bernoulli beam carrying concentrated masses. In order to estimate crack location and depth in the beam the proposed algorithm utilizes the variation of the difference between the natural frequencies of cracked and intact systems versus single mass location along the beam span. The assumed mode method is used to derive the mathematical model for the system under investigation, in which the crack's effect is introduced to the system as a global effect. The advantage of the proposed algorithm is to identify the crack by monitoring a single natural frequency of the system. The algorithm can utilize the measurements of the first few system natural frequencies to check/reconfirm its identification results. Furthermore, it is efficient and can be simply implemented for any structure that has a slowly moving mass, as in the case of overhead gantry and girder cranes. The identification algorithm is tested using the first system's natural frequency obtained from an experimental work as well as from a finite element analysis. Moreover, the algorithm is tested once more using the second system's natural frequency obtained from finite element analysis. The tests' results show that the crack depth and location can be predicted with sound accuracy.

Adaptive finite element analysis for damage detection of non-uniform Euler–Bernoulli beams with multiple cracks based on natural frequencies

“…Owolabi et al (2003) proposed that the location and size of a crack could be identified by finding changes in frequencies and amplitudes of frequency response functions. A beam with multiple cracks was modelled as a massless rotational spring or other models based on the Euler-Bernoulli theory, and this scheme was subsequently adopted for crack detection in stepped beams (Maghsoodi, et al, 2013;Al-Said, 2007, 2008. In most studies, the crack was assumed to be open and normal to the beam surface.…”

“…Lele and Maiti (2002) and Nikolakopoulos et al (1997) extended the frequency contour plot method to the crack detection in beams based on the Timoshenko beam theory and in-plane frame, respectively. In many cases, the three curves of the frequency contour plot unfortunately did not intersect because of the inaccuracy of modelling results as compared to measured results, and the zero-setting procedure was recommended for such cases (Maghsoodi, et al ., 2013; Al-Said, 2007, 2008; Morassi, 2001; Morassi, 2001). Narkis (1994) showed that if a crack is very small, the only information required for crack detection is the variation of the first two natural frequencies due to a crack.…”

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

“…Furthermore, the authors extended the studies also on intact stepped beams (Bambill et al, 2015; Su et al, 2018; Suddoung et al, 2014; Wattanasakulpong and Charoensuk, 2015), cracked homogeneous isotropic stepped beams (Al-Said, 2008; Attar, 2012; Kisa and Arif Gurel, 2007; Mao and Pietrzko, 2010; Naguleswaran, 2002; Nandwana and Maiti, 1997) and only one study on cracked FG stepped beams (Khiem et al, 2019).…”

Dynamic and experimental analysis on response of multi-cracked structures carrying transit mass

“…Zhu and Law 6 have proposed a damage identification method for the analysis of a damaged simply supported concrete bridge structure in the time-domain analysis using the vehicle bridge contact forces as base excitation. Al-Said 7 has developed a damage detection method in a stepped beam carrying a slowly moving load. Sekhar 8 has reviewed varieties of analysis on double and multi-cracked structures and studied the importance of damage detection technique in vibrating structures.…”