Vibration based crack analysis and detection in beams using energy method

• Main Author: Yang, Xinfeng, 1966-
• Other Authors: Memorial University of Newfoundland. Faculty of Engineering and Applied Science
• Format: Thesis
• Language: English
• Published: 2001
• Subjects: Girders > Vibration > Mathematical models; Girders > Cracking > Mathematical models; Newfoundland studies; University of Newfoundland
• Online Access: http://collections.mun.ca/cdm/ref/collection/theses3/id/147270

Thesis (Ph.D.)--Memorial University of Newfoundland, 2001. Engineering and Applied Science Bibliography: leaves 205-216. The thesis presents a comprehensive investigation on vibrations of cracked beam structures and methodologies for crack identification. In order to determine the crack influence on structural dynamic characteristics correctly and efficiently, a vibration model for cracked beams is developed. The crack model assumes that the crack is always open during the dynamic response of the structure and considers the reduction of stiffness at the crack location; in addition it also includes the influence of stress relief around the crack region and its influence on the effective stiffness around the crack location. -- Computation of stiffness for the cracked beam is achieved through consideration of strain energy variation in the structure, resulting from the occurrence of a crack. The model thus generates a continuous beam vibration equation (with varying moment of inertia), which could effectively incorporate the local changes of structural properties due to the crack. -- Using the model, vibration analyses of simply-supported and fixed-fixed solid rectangular beams, with one and two cracks, are carried out for computing natural frequencies and mode shapes. Changes of frequencies due to the crack are plotted considering crack size and/or crack location. It is shown that the natural frequencies would decrease as the crack size increases, and the decreases of frequencies would follow a wave-like pattern as the crack location changes. Comparisons are made with earlier results and some other experimental investigations, carried out for verifying some of these results, and shown to have a good agreement. -- Frequency contour procedure is developed for crack detection. Different combinations of crack sizes and locations would give different natural frequencies, and contour lines for the same normalized frequency (as that of the measured value of the corresponding mode) could be plotted. -- Frequency contours for different modes in a cracked structure (having values similar to the measured values) are plotted together, and the intersection point of all the contours provides the identification of the crack location and size. Analyses of a hollow beam model, representing a ship model, are also carried out. The beam model, with varying stiffness and mass, vibrates in water, generating added fluid mass of the ship model. Due to the eccentric nature of the added fluid mass and wave force excitation, both vertical bending vibration and coupled torsional-bending (horizontal) vibration are generated in the structure. Frequencies and mode shapes agree well with test results, obtained earlier in an experimental investigation. For a cracked backbone in the ship model, frequencies are obtained and plotted with crack size and crack location. The frequency contours are used to identify the crack size and location. -- To consider shear deformation and rotary inertia effect, the vibration analyses on Timoshenko beams, with/without a crack, are also carried out. The results are compared with that of Euler beams. -- Finally, forced vibration of cracked beams is considered. Frequency response, acceleration response and acceleration curvature response functions are obtained, and their changes due to a crack have been investigated. Acceleration curvature response and resonant acceleration amplitude procedures are found as suitable indicators to identify the crack.