Title page for ETD etd-08012012-040538

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
  • Rotational motion
Date of Defense 1989-03-29
Availability restricted
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


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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