Non-stationary motion of a cracked rotating shaft with accelerating or decelerating angular velocity Ω through a critical speed is studied. The shaft has a breathing transverse crack and a disk. There are two parts, which are the investigation of flexural response, neglecting the torsional vibrations, and the investigation of flexural-torsional response. In both studies the longitudinal vibration and the influence of shear deformation are neglected. The boundary conditions of the supports are simply supported for the transverse displacements and fixed-free in relation to torsion (for the flexural-torsional response only). The transverse surface crack, which causes a geometric discontinuity, is replaced by generalized moments at the crack location. The equations of motion follow the formulation of Wauer. Galerkin’s method and numerical integration are used to obtain approximate solutions. The maximum responses are determined. The effects of the acceleration and deceleration rate and the different parameters of the breathing cracked rotating shaft, such as crack depth, crack location, disk location, disk eccentricity, disk eccentricity angle, and disk mass, are studied. The influence of internal damping, external damping, and torsional external damping are investigated. Comparisons with an open cracked rotating shaft and an uncracked rotating shaft are also presented. The influence of torsional deformation is analyzed. The results are presented in tables and figures. / Master of Science

The detection of cracks in structural components and the evaluation of their sizes without the need of removing them from the machine in which they are placed is very important for preventing failures. The objective of this thesis is to study the effects of cracks on the dynamic behavior of shafts under acceleration or deceleration, in order to find methods or procedures capable of detecting the presence of cracks prior to failure. The equations of motion for a simply supported Bernoulli-Euler shaft are developed following Wauer's formulation. Galerkin's Method is used to obtain five-term approximate solutions. The first two natural frequencies are found for both the uncracked and cracked shaft. A computer program is written to perform the numerical integration of the equations. The shaft is subjected to several constant accelerations and decelerations. Tables and figures showing the results are presented along with discussions and comments related to the different runs made and the results obtained. The effect of the initial position angle of the eccentricity is studied to find the influence of this parameter. The effects of crack position and crack depth on the dynamic behavior of the shaft are also included in this work. Time histories and summary graphs are presented to make easier the interpretation of the results. Final conclusions and future research proposals complete the work done in this thesis. / Master of Science