Energy due to fluid-borne and structure-borne disturbances propagating in a fluid-filled pipe will be carried by the structure and the fluid. Energy transfer may occur between these two media due to the coupling between the structure and the fluid. It's not clear when the excitation is fluid-borne or structure-borne, due to the complexity in piping installation designs and the strong coupling between the fluid and shell walls. It is necessary to devise control approaches that tackle both components of the excitation simultaneously. This study will demonstrate new approaches in active and passive control techniques and show their advantages over classical control approaches. It is necessary to understand the physical behavior of fluid-filled pipes, in order to develop a viable control methodology. The equations of motion for the shell and the fluid are needed to characterize the system. These combined with the dispersion equations can then be used to derive analytical expressions for energy flow in the system. The research is limited to lower order wave types. Hence, the expressions for energy flow are derived only for the n=0 and n=1 shell waves and n=0 fluid wave. Higher order waves have cut-on frequencies and were not analyzed. Current sensing methodologies are limited to the analysis of wave types separately. A new approach of wave decomposition using multiple sensors is developed and used to characterize discontinuities along the pipe. The effect of discontinuities and correct control methodologies are investigated. A new control methodology is developed and implemented. The natural distribution of energy into different wave types as it encounters discontinuities is used to devise control solutions with non-intrusive inertial actuators. Improvements of 16 dB in shell waves and 12 dB in fluid waves over the correct control approach are experimentally demonstrated. / Master of Science

Experimental results concerning plasma turbulence pumped in theionosphere by powerful radio waves suggest that the turbulence is due todeterministic chaos. To investigate the possibility of deterministic chaosin the ionosphere coupled wave systems have been studied to see chaoticdynamics. If coupled waves can exhibit chaos it is a possible way tomodel ionospheric chaos. The result showed that chaos was present inboth wave systems studied which means that they could possibly explainthe chaos, to verify this more studies needs to be done on theparameters relevant to the coupled wave systems in the ionosphere andfind if they are in a regime where chaos develops / Studier av plasmaturbulens i jonosfären som pumpas av kraftfulla radiovågor antyder att turbulensen är kopplat till deterministiskt kaos. För att undersöka möjligheten för deterministiskt kaos i jonosfären studeras kopplade vågsystem om de kan innehålla kaotiska regimer. Om dessa system visar kaotiskt beteende skulle de kunna användas för att beskriva kaos i jonosfären. Resultatet visade att kaos var närvarande i de kopplade vågsystem som studerats, för att verifiera om de kan användas för att beskriva kaos i jonosfären måste närmare studier av de parametrar som modellen använder sig av göras för att se om de faller inom ett intervall där kaos uppstår.

This thesis has two parts: In the first part, we study the dispersion characteristics of structural-acoustic waveguides by obtaining closed-form solutions for the coupled wave numbers. Two representative systems are considered for the above study: an infinite two-dimensional rectangular waveguide and an infinite fluid- filled orthotropic circular cylindrical shell. In the second part, these asymptotic expressions are used to study the nonlinear wave propagation in the same two systems. The first part involves obtaining asymptotic expansions for the fluid-structure coupled wave numbers in both the systems. Certain expansions are already available in the literature. Hence, the gaps in the literature are filled. Thus, for cylindrical shells even in vacuo wavenumbers are obtained as part of the objective. Here, singular and regular perturbation methods are used by taking the thickness parameter as the asymptotic parameter. Valid wavenumber expressions are obtained at all the frequencies. A transition in the behavior of the flexural wavenumbers occurs in the neighborhood of the ring frequency. This frequency of transition is identified for the orthotropic shells also. The closed-form expressions for the orthotropic shells are obtained in the limit of slight orthotropy for the circumferential orders n > 0 at all the frequency ranges. Following this, we derive the coupled wavenumber expressions for the two systems for an arbitrary fluid loading. Here, the two-dimensional rectangular waveguide is considered first. This rectangular waveguide has a one-dimensional plate and a rigid surface as its lateral boundaries. The effects due to the structural boundary are studied by analyzing the phase change due to the structure on an incident plane wave. The complications due to the cross-sectional modes are eliminated by ignoring the presence of the other rigid boundary. Dispersion characteristics are predicted at various regions of the dispersion diagram based on the phase change. Moreover, the also identified. Next, the rigid boundary is considered and the coupled dispersion relation for the waveguide is solved for the wavenumber expressions. The coupled wavenumbers are obtained as the coupled rigid-duct, the coupled structural and the coupled pressure-release wavenumbers. Next, based on the above asymptotic analysis on a two-dimensional rectangular waveguide, the asymptotic expansions are obtained for the coupled wavenumbers in isotropic and orthotropic fluid- filled cylindrical shells. The asymptotic expansions of the wavenumbers are obtained without any restriction on the fluid loading. They are compared with the numerical solutions and a good match is obtained. In the second part or the nonlinear section of the thesis, the coupled wavenumber expressions are used to study the propagation of small but a finite amplitude acoustic potential in the above structural-acoustic waveguides. It must be mentioned here that for the rst time in the literature, for a structural-acoustic system having a contained fluid, both the structure and the acoustic fluid are nonlinear. Standard nonlinear equations are used. The focus is restricted to non-planar modes. The study of the cylindrical shell parallels that of the 2-D rectangular waveguide, except in that the former is more practical and complicated due to the curvature. Thus, with regard to both systems, a narrow-band wavepacket of the acoustic potential centered around a frequency is considered. The approximate solution of the acoustic velocity potential is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that the amplitude modulation is governed by the Nonlinear Schr•odinger equation (NLSE). The nonlinear term in the NLSE is analyzed, since the sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. This sign change is predicted using the coupled wavenumber expressions. Secondly, at specific frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonic. This happens when the phase speeds of the waves match. The frequencies of such interactions are identified, again using the coupled wavenumber expressions. The novelty of this work lies firstly in considering nonlinear acoustic wave prop-agation in nonlinear structural waveguides. Secondly, in deriving the asymptotic expansions for the coupled wavenumbers for both the two-dimensional rectangular waveguide and the fluid- filled circular cylindrical shell. Then in using the same to study the behavior of the nonlinear term in NLSE. And lastly in identifying the frequencies of nonlinear interactions in the respective waveguides.