have concentrated on detecting multiple cracks in beams by vibration measurements, and presented some methods. Yan and Ren gave the closed form of the sensitivity of modal flexibility by eigenvalue and eigenvector derivatives, and adopted it to calculate damage locations and extents. utilized hybrid sensitivity matrices for damage detection in axially functionally graded beams. Their method can locate damage under varying environment conditions. employed mode shape curvatures for damage locations and used them as a vibration feature in conjunction with principal component analysis for the first time. In addition, many other intelligent optimization methods such as moth-flame algorithm, bee colony algorithm and grey wolf algorithm have been applied to structural damage detection problem. Ghannadi and Kourehli developed a new objective function and minimized the function by salp swarm algorithm to detect damages in multi-story shear frames. Then, extents of damaged elements are calculated by a modified genetic algorithm. In the first stage, elements that are most likely damaged are found by the modal strain energy. exploited the modal strain energy for damage detection.
#FLEXIBILITY METHOD OF STRUCTURAL ANALYSIS EXAMPLES FULL#
Vibration-based methods make full use of changes in the frequency-domain modal properties, such as natural frequencies, mode shapes and its curvatures, modal flexibility and its derivatives, modal strain energy and frequency response function. As natural frequencies and mode shapes depend on structural parameters, changes in them can be an effective indication of structural deterioration. Engineers and researchers, especially in fields of aerospace and offshore oil, have begun to use vibration-based methods from the late 1970s and early 1980s. Īmong these detection methods, vibration-based methods have attracted much attention. Over last few decades, some techniques such as wave propagation, impedance change and ultrasonic inspection have been employed, and various methods have been proposed for the damage detection. Thus finding these damages via nondestructive techniques at the earliest possible stage is very important. If these damages cannot be found as soon as possible, they will cause the structure to work ineffectively and may lead to a disaster. During their service life cycles, they may be damaged due to the adverse impact of environmental factors. Many engineering structures such as bridges, buildings, dams and pipelines support a society’s economic prosperity and quality of life.