Tumble mills are hollow cylindrical shells of large diameter carrying grinding media (a combination of rock/iron ore/chemical flakes and metal balls/rods), which, upon rotation of the mill, will be ground into fine powder. These mills rotate at low speeds using a gear reduction unit and often have vibration problems. These vibration problems result in increased gear wear and occasional catastrophic failures resulting in production loss. The objective of this research is to investigate the effect of oscillation of grinding media on torsional vibrations of the mill. A theoretical model was developed to determine the oscillating frequency of the grinding media. A 12" (0.3 m) diameter tumble mill test rig was built with a 0.5 hp DC motor. The rig is tested with sand and iron bb balls to simulate the industry process application. At low volume levels the grinding media oscillates like a rigid body as compared to higher volumes. It is shown that tumbling action of grinding media causes torsional excitation and hence its effect has to be considered in torsional vibration analysis. At starting, the load on the gears is much higher due to this oscillation.

Free vibration of composite piezoelectric transducers is analyzed by a modified two-dimensional axisymmetric finite element in this study. The modified finite element is formulated based on assumed displacement fields and electric potential, and is capable for three-dimensional analyses of vibration of axisymmetric composite piezoelectric structures. Different arrangements and radius of piezoelectric disk and metal ring, with various thicknesses will be considered and first radial vibration frequencies are derived and their mode shapes are demonstrated, which might be helpful for the design of radial composite transducers. Also, the results of the present study will be compared with those by other methods.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1991. / Vita. Abstract. Includes bibliographical references (leaves 170-175). Also available via the Internet.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 77-80).

Thesis (M.S.)--University of Delaware, 2009. / Principal faculty advisor: Henry R. Glyde, Dept. Physics & Astronomy. Includes bibliographical references.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Cam follower -- dynamic modeling -- vibration -- follower jump. Includes bibliographical references (p. 98-102).

Thesis (M.S. in Mechanical Engineering)--Washington State University. / Includes bibliographical references.

Thesis (doktor-ingenieur)--Technische hochschule, Stuttgart. / Lebenslauf. "Literaturverzeichnis": p. 7-8.

Thesis (Ph. D.)--Lehigh University, 2001. / Includes vita. Includes bibliographical references (leaves 139-146).

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, June 2003. / Thesis advisor(s): Young S. Shin, Ilbae Ham. Includes bibliographical references (p. 49). Also available online.