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

As an extension of previously reported work on effects of internal resonance on non-linear vibration of beams, it has been shown that for blade-like beams excited parametrically by support motion in the plane of maximum stiffness, complex combination instabilities are observed. In addition to the well-known sum-type combination instability existing between the fundamental out-of-plane bending and the torsional modes of the beam, investigation has revealed the occurrence of higher order instabilities producing detectable bending and torsional vibrations which are not synchronous with external excitations. These effects are subsequently shown to exist in a related way in coupled beam configurations shown to exist in a related way in coupled beam configurations under forced vibration when specific internal resonance conditions exist between the natural frequencies of the various modes, and to produce visible patterns of non-linear energy flow between modes. This study considers one such effect both experimentally and theoretically, consisting predominantly of a coupling between the fundamental and second nonplanar bending modes, and torsion mode. This combination resonance was modelled by taking the perturbation analysis to second order and including other contributory terms in the system governing equations. An expression for the transition curve for this resonance has been derived which shows the regions of stable and unstable solutions in a two parameter plane. Very close agreement is obtained between theoretical and experimental results for different beam lengths. It is also shown that if the geometry of the system is such that theses two combination resonances can be excited simultaneously, very small alternations to the internal tuning of the system can generate noticeable intermodal energy exchange effects. This system is then examined in the context of non-linear forced vibration and to this end an arrangement of coupled beams is studied. The vertical blade-like beam is coupled to the free end of a horizontal cantilever beam which is externally excited at a frequency in the region of its second bending mode frequency. This allows for the possibility of four mode interaction between the three nonplanar modes described above and also the second planar bending mode. A four-degree-of-freedom model was formulated and perturbation analysis revealed that complex multimodal responses could occur for a single-frequency excitation. Steady-state solutions were derived by means of numerical integration techniques. A reasonable degree of agreement was observed between theoretical and experimental results.

Thesis (M. Eng. Sc.)--University of Adelaide, Dept. of Mechanical Engineering, 1999. / Includes bibliographical references (leaves 94-97).

Thesis (M.Eng.Sc.)--University of Adelaide, Dept. of Mechanical Engineering, 1999. / Bibliography: leaves 94-97.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (leaves 181-184).

Thesis (M.S.)--Tennessee Technological University, 2009. / Title from title page screen (viewed on Mar. 18, 2010). Bibliography: leaves 69-72.

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, June 2004. / Thesis advisor(s): Young S. Shin. Includes bibliographical references (p. 69-70). Also available online.

Thesis(M.S.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references.

Thesis (M.S.)--Rochester Institute of Technology, 1995. / Typescript. Includes bibliographical references (leaves 97-99).

This thesis represents the work that has been done by the author during his Master of Engineering Science candidature in the area of vibration control of flexible structures at the School of Mechanical Engineering, The University of Adelaide, between March 2003 and June 2004. The aim of this research is to further extend the application of the Spatial Control Approach for two-dimensional flexible structures for attenuating global structural vibration with the possible implication of reduction in noise radiation. The research was concentrated on a simply supported thin flexible plate, using piezoelectric ceramic materials as actuators and sensors. In this work, active controllers were designed for the purpose of controlling only the first five vibration modes (0-500Hz) of the plate. A spatial controller was designed to minimize the total energy of the spatially distributed signal, which is reflected by the spatial H2 norm of the transfer function from the disturbance signal to the vibration output at every point over the plate. This approach ensures the vibration contributed by all the in bandwidth (0-500 Hz) vibration modes is minimized, and hence is capable of minimizing vibration throughout the entire plate. Within the control framework, two cases were considered here; the case when the prior knowledge of the incoming disturbance in terms of reference signal is vailable and the case when it is not available. For the case when the reference signal is available, spatial feedforward controller was designed; whereas for the case when the reference signal is not available, spatial feedback controller was designed to attenuate the global disturbance. The effectiveness of spatial controllers was then compared with that of the standard point-wise controllers numerically and experimentally. The experimental results were found to reflect the numerical results, and the results demonstrated that spatial controllers are able to reduce the energy transfer from the disturbance to the structural output across the plate in a more uniform way than the point-wise controllers. The research work has demonstrated that spatial controller managed to minimize the global plate vibrations and noise radiation that were due to the first five modes. / Thesis (M.Eng.Sc.)--School of Mechanical Engineering, 2005.