Identifying the Number of the Bilinear Cracks in the Frame Structures

In many vibration-based methods, stiffness matrix variations play an important role in determining the location and extent of damage. In this research, through a bilinear crack model, stiffness matrix components are directly linked to the cracking parameters with the aid of seven coefficients. An innovative method for identifying the number of breathing cracks is developed, in a manner that the information of the initial structure is not needed. To model structures in MATLAB software, a nonlinear dynamic analysis program with the ability to model bilinear cracks is developed. Breathing crack modeling has been done using the softness method and the concept of curvature of the member. In order to determine the open or closed state of the crack, at each moment of vibration, an indicator was applied based on the moment curvature of each element. Due to the crack opening and closure, frequency varies continuously over time. If there is only one crack in the structure, two frequency values for the first mode of vibration are obtained. It is clear that one is related to when the crack is open and the other corresponds to when the crack is closed. By increasing the number of cracks, the number of frequency bands increases nonlinearly. This feature applied to determine the number of damaged points, so that the vibration frequencies were determined and arranged throughout the vibration time. By plotting the ordered frequencies, the points of the same frequency were plotted at a certain level and formed the frequency steps. A significant relationship was found between the number of frequency steps and cracked points. By applying different crack topography in buildings of one, two and five stories, a relationship between frequency steps and number of cracks was formulated. In each incident scenario, the effect of different crack intensity and distribution is investigated through three different cases. The first case is, 20 different crack layouts with a depth of 0.1 of the cross sectional area and random distribution, the second case is, 20 different crack layouts with a depth of 0.3 of the cross sectional area and random distribution, and the last case is, 20 different layouts in which the location and depth of the crack as well as the crack propagation are considered random. The average and standard deviation of frequency steps for each 20 tries are obtained. This study shows that, the variation of frequency steps in terms of the cracks number is similar in different structures. The uniform change of the depth of all cracks is ineffective in increasing the number of frequency steps. However, diversifying cracking due to the combination of asymmetric distribution, increases the number of frequency steps. When about half of the members are cracked, the maximum standard deviation of frequency steps occurs. This dispersion reduces the identification accuracy up to two crack numbers in the studied structures. The curve of variation of frequency steps in terms of the number of cracks is divided into two parts. The first part of the curve is as long as the number of cracks is less than half of the number of members. At this region, the exponential relationship between the two parameters is established. The second part of the curve is when more than half of the number of members are cracked. In this case, the frequency steps show little changes with the change in the number of cracks. In this region, the relationship between the two parameters is different for each structure, but it has a trend of quadratic order. Some of the factors such as axial force which can change the stiffness of the frames at any moment of vibration can affect the number of frequency steps. Investigating the effect of these factors can be the subject of future research.