Type of Document	Master's Thesis
Author	Collins, Kevin Ralph
URN	etd-08012012-040538
Title	The effect of cracks on the dynamic behavior of bars and shafts
Degree	Master of Science
Department	Civil Engineering
Advisory Committee	Advisor Name Title Plaut, Raymond H. Committee Chair Holzer, Siegfried M. Committee Member Rojiani, Kamal B. Committee Member
Keywords	Rotational motion
Date of Defense	1989-03-29
Availability	restricted
Abstract Nondestructive methods of detecting cracks in structural components and machinery are important, both in preventing failures and in establishing maintenance procedures. This thesis considers how the vibration behavior of cracked members can be modelled mathematically and how these mathematical models may lead to advancements in crack detection procedures. Two separate cases are considered: the longitudinal vibration of a cracked bar and the coupled vibrations of a cracked rotating shaft. In the longitudinal vibration study, the equation of motion is developed for a cantilevered bar with a symmetric surface crack. Next, Galerkin's Method is used to obtain one- and two-term approximate solutions. Both forced and free vibrations of the bar are analyzed. Graphical results showing the relationships between displacement and crack size, crack position, and forcing frequency are presented and discussed. Spectral analysis is used to compare uncracked and cracked bar behavior. Finally, a sensitivity analysis of the forced vibration case is conducted to observe how the forcing frequency affects the rate of change of steady-state response at the onset of cracking. In the second part of the thesis, a similar analysis is conducted for a cracked, simply-supported Timoshenko shaft rotating at a constant angular speed. The equations of motion derived by Wauer (b) are used as the basis of the study. Again, Galerkin's Method is applied to obtain approximate solutions. Time histories and spectra are used to observe how changes in various parameters influence the vibration behavior. The effects of mass eccentricity and gravity are studied. Finally, the effect of a periodic axial impact load is considered.
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