published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 106-108).

Thesis (M.S.)--Rochester Institute of Technology, 2007. / Typescript. Includes bibliographical references (leaves 67-68).

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C.T.G. Looney proposed a method of solving the problem of steady-state forced vibration of continuous frames. Starting with the analysis of a single span, simply supported beam, the method was extended to continuous beams and frames. An investigation of his method was undertaken comparing experimental deflection with those predicted by Looney’s method. A single span beam and a two span continuous beam was used in the experiment. A mechanical shaker was used to vibrate the beam. The experimental and nautical curves showed good agreement with the experimental values being consistently higher. Although the weight of the shaker's moving parts was less than one-tenth the weight of the beam it had considerable effect in lowing the resonant frequency and increasing amplitudes. / M.S.

The purpose of this thesis has been to investigate the influence of secondary effects for beams resting on elastic foundations and vibrating beams. Two problems have been presented for beams on elastic foundations and a general comparison has been made for an infinite vibrating beam. / Master of Science

As a suggestion for further work in deriving the equations by the Principle of Virtual Displacements, it might be advisable to write the equations based on the vertical displacements of the points of inflection of each column. The concentrated mass of each panel would be located at the center of the respective columns. This appears to be a better approximation than concentrating each mass at the lower joint. / Master of Science

Active control of flexural power flow in infinite, semi-infinite and finite beams by point force inputs has been analytically and experimentally studied. The systems were analyzed by assuming wave solution and then applying various terminating boundary conditions. Optimal control solutions were then obtained using a quadratic Wiener solution. The influence of system parameters such as discontinuity impedance and effects such as near fields, number and location of control actuators and error sensors is investigated and discussed. The mechanisms by which control is achieved are considered. It is demonstrated that the boundary conditions and the system configuration strongly influence the choice of optimal controller format. The experimental work is compared with the theoretical developments and found to be in good agreement. Control was achieved by a LMS Filtered-x algorithm implemented in assembler language on a TMS32020 digital signal processing chip. In general it is demonstrated that the flexural power flow in the beam types considered can be attenuated with a low number of active actuators. / Master of Science