The flow field behavior in the vicinity of a perforated breakwater and the efficiency of the breakwater under regular waves were studied. To examine the efficiency of the structure thirteen types of regular wave conditions with wave periods T = 1, 1.2, 1.6, 2, 2.5 sec and wave heights Hi = 2, 4, 6, 8, 10 cm in an intermediate water depth of 50 cm were tested. The incoming, reflected and transmitted wave heights were measured using resistance type wave gauges positioned at the required locations. The efficiency of the structure was calculated considering the energy balance for the system. The efficiency of the structure for different wave conditions and with different parameters are shown and compared. Seven types of regular waves with wave periods T = 1, 1.6, 2, 2.5 sec and wave heights Hi = 4, 6, 8, 10 cm in an intermediate water depth of 50 cm were tested for the flow behavior study. In order to study the flow field variation with phase, ten phases were considered per one wave. The Particle Image Velocimetry (PIV) technique was employed to measure the two dimensional instantaneous velocity field distribution and MPIV (Matlab toolbox for PIV) and DaVis (a commercial software) were used to calculate the velocity vectors. By repeating the experiments and taking an average, the mean velocity field, mean vorticity field, mean turbulent intensity and mean turbulent kinetic energy field were calculated for each phase and for each wave condition. The phase average fields for each wave condition for each of the above mentioned parameters were calculated taking the average of ten phases. The phase averaged velocity, vorticity and turbulent kinetic energy fields are presented and compared. The energy dissipation based on both elevation data and the velocity data are presented and compared. It was found that for more than 75% of the tested wave conditions, the energy dissipation was above 69%. Thus the structure is very effective in energy dissipation. Further it was found that for all the tested wave conditions most of the turbulent kinetic energy form near the free surface and near the front wall, where as behind the back wall of the structure the turbulent kinetic energy was very small.

The flow field behavior in the vicinity of a perforated breakwater and the efficiency of the breakwater under regular waves were studied. To examine the efficiency of the structure thirteen types of regular wave conditions with wave periods T = 1, 1.2, 1.6, 2, 2.5 sec and wave heights Hi = 2, 4, 6, 8, 10 cm in an intermediate water depth of 50 cm were tested. The incoming, reflected and transmitted wave heights were measured using resistance type wave gauges positioned at the required locations. The efficiency of the structure was calculated considering the energy balance for the system. The efficiency of the structure for different wave conditions and with different parameters are shown and compared. Seven types of regular waves with wave periods T = 1, 1.6, 2, 2.5 sec and wave heights Hi = 4, 6, 8, 10 cm in an intermediate water depth of 50 cm were tested for the flow behavior study. In order to study the flow field variation with phase, ten phases were considered per one wave. The Particle Image Velocimetry (PIV) technique was employed to measure the two dimensional instantaneous velocity field distribution and MPIV (Matlab toolbox for PIV) and DaVis (a commercial software) were used to calculate the velocity vectors. By repeating the experiments and taking an average, the mean velocity field, mean vorticity field, mean turbulent intensity and mean turbulent kinetic energy field were calculated for each phase and for each wave condition. The phase average fields for each wave condition for each of the above mentioned parameters were calculated taking the average of ten phases. The phase averaged velocity, vorticity and turbulent kinetic energy fields are presented and compared. The energy dissipation based on both elevation data and the velocity data are presented and compared. It was found that for more than 75% of the tested wave conditions, the energy dissipation was above 69%. Thus the structure is very effective in energy dissipation. Further it was found that for all the tested wave conditions most of the turbulent kinetic energy form near the free surface and near the front wall, where as behind the back wall of the structure the turbulent kinetic energy was very small.

Periodically perforated sheets(PS) are ubiquitous in nature as well as in engineered artifacts developed for aerospace, automotive, marine, nuclear and structural applications. PS are indispensable for saving weight and cost for aircraft; for enhancing safety and integrity of heat exchangers used in nuclear and thermal power stations. Ancient PS grills and lattice frames dating back to 1000 BC continue to inspire contemporary art and architecture, buildings and furniture. PS design and analysis, however, is a complex affair stemming from the inherent configurational anisotropy induced by periodicity. In addition, complex boundary conditions complicate the analysis. Unlike atoms in crystalline media, both shape and periodicity of perforations control this anisotropic nature. This thesis explores theoretical and numerical strategies for evaluating the effective anisotropic elastic moduli of PS. Following an experimental prelude for visualizing the PS stress field in a photoelastic sheet and a brief review of PS theory, this thesis proposes a novel theoretical numerical hybrid method for determining the Airy stress function constants. The proposed hybrid method can be exploited experimentally using automated vision based imaging technologies to measure the boundary displacements noninvasively. For determining the Airy constants periodic boundary conditions to the unit cell are applied, the displacement components around the PS hole boundary are obtained using FEM. Using these constants the PS stress field is reconstructed to assess the efficacy of the proposed hybrid method. It is observed that in general while the actual and the reconstructed stress fields agree reasonably well, more refined boundary data obtained either numerically or experimentally can enhance the accuracy further. The thesis then makes an extensive presentation of anisotropic moduli in a variety of PS designs configured on rectangular or square layouts. Conventional as well as some exotic patterns with cusps and satellite holes are examined, and the results are presented graphically to aid the designer. Finally, some special topics pertaining PS design and analysis are discussed to help overcome the inherent limitations of solutions based on applying periodic boundary conditions. In this vein, strategies for achieving a functionally graded PS are presented by altering the pitch and hole size. These strategies assume importance near boundaries as well as near concentrated forces inducing stress gradients. Other special topics include the applicability of tensor transformation rule to PS anisotropy. The effective bulk modulus which remains a scalar invariant is exploited to assess the validity of tensor transformation in a square PS. The rule of mixture widely used in homogenization of composite media is also discussed briefly. Thus, this thesis makes an attempt to demonstrate the power of blending micromechanics with experiments and FEM to aid in PS design and analysis.

Multiscale phenomena implicitly appear in every physical model. The understanding of the general behavior of a given model at different scales and how one can correlate the behavior at two different scales is essential and can offer new important information. This thesis describes a series of new techniques and results in the analysis of multi-scale phenomena arising in PDEs on variable geometries. In the Second Chapter of the thesis, we present a series of new error estimate results for the periodic homogenization with nonsmooth coefficients. For the case of smooth coefficients, with the help of boundary layer correctors, error estimates results have been obtained by several authors (Oleinik, Lions, Vogelius, Allaire, Sarkis). Our results answer an open problem in the case of nonsmooth coefficients. Chapter 3 is focused on the homogenization of linear elliptic problems with variable nonsmooth coefficients and variable domains. Based on the periodic unfolding method proposed by Cioranescu, Damlamian and Griso in 2002, we propose a new technique for homogenization in perforated domains. With this new technique classical results are rediscovered in a new light and a series of new results are obtained. Also, among other advantages, the method helps one prove better corrector results. Chapter 4 is dedicated to the study of the limit behavior of a class of Steklov-type spectral problems on the Neumann sieve. This is equivalent with the limit analysis for the DtN-map spectrum on the sieve and has applications in the stability analysis of the earthquake nucleation phase model studied in Chapter 5. In Chapter 5, a $Gamma$-convergence result for a class of contact problems with a slip-weakening friction law, is described. These problems are associated with the modeling of the nucleation phase in earthquakes. Through the $Gamma$-limit we obtain an homogenous friction law as a good approximation for the local friction law and this helps us better understand the global behavior of the model, making use of the micro-scale information. As to our best knowledge, this is the first result proposing a homogenous friction law for this earthquake nucleation model.

Typescript, etc. / Digitized by Kansas Correctional Industries

Large electric transformers such as those used in high voltage substations radiate an annoying low frequency hum into nearby communities. Attempts have been made to actively control the noise by placing a large number of loudspeakers as control sources around noisy transformers to cancel the hum. These cancellation systems require a large number of loudspeakers to be successful due to the imposing size of the transformer structures. Thus such systems are very expensive if global noise reduction is to be achieved. The aim of this thesis is to investigate theoretically and experimentally the use of thin perforated panels closely placed to a heavy structure to reduce the radiation of unwanted harmonic noise. These panels can themselves be vibrated to form a control source radiating over a large surface surrounding the primary source. The problem of the equipment overheating inside the enclosure is alleviated because the holes in the panels still allow natural cooling. An initial study is carried out to determine the resonance frequencies of perforated panels. The use of previously determined effective elastic properties of the panels and Finite Element Analysis to theoretically calculate their resonance frequencies is examined. Secondly the attenuation provided by active noise control using perforated panels as control sources is explored by use of a coupled analysis, where the primary source is assumed to influence the radiation of the perforated control panel. This analysis was found to predict poorly the amount of attenuation that could be achieved, so an uncoupled analysis is undertaken, where both the primary and control sources are assumed to radiate independently of each other. Not only does this greatly simplify the theoretical analysis but it also enables prediction of attenuation levels which are comparable to those determined experimentally. The theoretical model is reformulated to enable comparison of the sound power attenuation provided by perforated panel control sources with that of traditional acoustic and structural control sources. Finally, the use of modal filtering of traditional acoustic error sensor signals to give transformed mode (or power mode) sensors is examined. The independently radiating acoustic transformed modes of the panel are determined by an eigenanalysis and a theoretical analysis is presented for a farfield acoustic power sensor system to provide a direct measurement of the total radiated acoustic power. The frequency dependence of the sensor system, and the amount of global sound power attenuation that can be achieved is examined. Experimental measurements are made to verify the theoretical model and show that a sound power sensor implemented with acoustic sensors can be used in a practical active noise control system to increase the amount of attenuation that can be achieved. Alternatively the sound power sensor can be used to reduce the number of error channels required by a control system to obtain a given level of attenuation when compared to traditional error criteria. The power mode sensor analysis is then applied to the perforated panel control system, with similar results. / Thesis (Ph.D.)--Engineering (Department of Mechanical Engineering), 1996.

Large electric transformers such as those used in high voltage substations radiate an annoying low frequency hum into nearby communities. Attempts have been made to actively control the noise by placing a large number of loudspeakers as control sources around noisy transformers to cancel the hum. These cancellation systems require a large number of loudspeakers to be successful due to the imposing size of the transformer structures. Thus such systems are very expensive if global noise reduction is to be achieved. The aim of this thesis is to investigate theoretically and experimentally the use of thin perforated panels closely placed to a heavy structure to reduce the radiation of unwanted harmonic noise. These panels can themselves be vibrated to form a control source radiating over a large surface surrounding the primary source. The problem of the equipment overheating inside the enclosure is alleviated because the holes in the panels still allow natural cooling. An initial study is carried out to determine the resonance frequencies of perforated panels. The use of previously determined effective elastic properties of the panels and Finite Element Analysis to theoretically calculate their resonance frequencies is examined. Secondly the attenuation provided by active noise control using perforated panels as control sources is explored by use of a coupled analysis, where the primary source is assumed to influence the radiation of the perforated control panel. This analysis was found to predict poorly the amount of attenuation that could be achieved, so an uncoupled analysis is undertaken, where both the primary and control sources are assumed to radiate independently of each other. Not only does this greatly simplify the theoretical analysis but it also enables prediction of attenuation levels which are comparable to those determined experimentally. The theoretical model is reformulated to enable comparison of the sound power attenuation provided by perforated panel control sources with that of traditional acoustic and structural control sources. Finally, the use of modal filtering of traditional acoustic error sensor signals to give transformed mode (or power mode) sensors is examined. The independently radiating acoustic transformed modes of the panel are determined by an eigenanalysis and a theoretical analysis is presented for a farfield acoustic power sensor system to provide a direct measurement of the total radiated acoustic power. The frequency dependence of the sensor system, and the amount of global sound power attenuation that can be achieved is examined. Experimental measurements are made to verify the theoretical model and show that a sound power sensor implemented with acoustic sensors can be used in a practical active noise control system to increase the amount of attenuation that can be achieved. Alternatively the sound power sensor can be used to reduce the number of error channels required by a control system to obtain a given level of attenuation when compared to traditional error criteria. The power mode sensor analysis is then applied to the perforated panel control system, with similar results. / Thesis (Ph.D.)--Engineering (Department of Mechanical Engineering), 1996.

Large electric transformers such as those used in high voltage substations radiate an annoying low frequency hum into nearby communities. Attempts have been made to actively control the noise by placing a large number of loudspeakers as control sources around noisy transformers to cancel the hum. These cancellation systems require a large number of loudspeakers to be successful due to the imposing size of the transformer structures. Thus such systems are very expensive if global noise reduction is to be achieved. The aim of this thesis is to investigate theoretically and experimentally the use of thin perforated panels closely placed to a heavy structure to reduce the radiation of unwanted harmonic noise. These panels can themselves be vibrated to form a control source radiating over a large surface surrounding the primary source. The problem of the equipment overheating inside the enclosure is alleviated because the holes in the panels still allow natural cooling. An initial study is carried out to determine the resonance frequencies of perforated panels. The use of previously determined effective elastic properties of the panels and Finite Element Analysis to theoretically calculate their resonance frequencies is examined. Secondly the attenuation provided by active noise control using perforated panels as control sources is explored by use of a coupled analysis, where the primary source is assumed to influence the radiation of the perforated control panel. This analysis was found to predict poorly the amount of attenuation that could be achieved, so an uncoupled analysis is undertaken, where both the primary and control sources are assumed to radiate independently of each other. Not only does this greatly simplify the theoretical analysis but it also enables prediction of attenuation levels which are comparable to those determined experimentally. The theoretical model is reformulated to enable comparison of the sound power attenuation provided by perforated panel control sources with that of traditional acoustic and structural control sources. Finally, the use of modal filtering of traditional acoustic error sensor signals to give transformed mode (or power mode) sensors is examined. The independently radiating acoustic transformed modes of the panel are determined by an eigenanalysis and a theoretical analysis is presented for a farfield acoustic power sensor system to provide a direct measurement of the total radiated acoustic power. The frequency dependence of the sensor system, and the amount of global sound power attenuation that can be achieved is examined. Experimental measurements are made to verify the theoretical model and show that a sound power sensor implemented with acoustic sensors can be used in a practical active noise control system to increase the amount of attenuation that can be achieved. Alternatively the sound power sensor can be used to reduce the number of error channels required by a control system to obtain a given level of attenuation when compared to traditional error criteria. The power mode sensor analysis is then applied to the perforated panel control system, with similar results. / Thesis (Ph.D.)--Engineering (Department of Mechanical Engineering), 1996.

Erosion, transportation, and deposition of sediment into receiving waters can have substantial environmental and economic impacts. Sedimentation basins are a remediation technique used to limit sediment transport from earth disturbance activities. Retention efficiency is used as a measure of a sedimentation basin's effectiveness. Several factors influence retention efficiency including the type of principal spillway used. The most common spillway is the perforated riser which dewaters the basin throughout its entire vertical profile. However, a relatively new outlet device, the skimmer, has been developed, which dewaters the basin from the water surface. A laboratory study was conducted to compare the skimmer with the perforated riser for three different soil types and determine if there were any significant differences in the trapping efficiencies of the two outlets. The test basin dewatered over a three hour period. The parameters observed were dewatering rate, effluent sediment concentration, sediment loss rate, and retention efficiency. The skimmer treatments consistently had higher values of sediment retention efficiencies. A statistical analysis performed on the retention efficiency data showed that retention efficiency was not influenced by any combination of outlet and soil type and that outlet was significant at the 5% level. Overall, the skimmer outperformed the perforated riser for all soil types tested. Additionally, retention efficiencies were predicted for shorter dewatering times. The results indicated shorter dewatering times may have smaller impacts on the retention efficiency of basins where the skimmer is utilized rather than the perforated riser. / Master of Science

The study of normal impedance of perforated plate acoustic liners including the effect of bias flow was studied. Two impedance models were developed, by modeling the internal flows of perforate orifices as infinite tubes with the inclusion of end corrections to handle finite length effects. These models assumed incompressible and compressible flows, respectively, between the far field and the perforate orifice. The incompressible model was used to predict impedance results for perforated plates with percent open areas ranging from 5% to 15%. The predicted resistance results showed better agreement with experiments for the higher percent open area samples. The agreement also tended to deteriorate as bias flow was increased. For perforated plates with percent open areas ranging from 1% to 5%, the compressible model was used to predict impedance results. The model predictions were closer to the experimental resistance results for the 2% to 3% open area samples. The predictions tended to deteriorate as bias flow was increased. The reactance results were well predicted by the models for the higher percent open area, but deteriorated as the percent open area was lowered (5%) and bias flow was increased. A fit was done on the incompressible model to the experimental database. The fit was performed using an optimization routine that found the optimal set of multiplication coefficients to the non-dimensional groups that minimized the least squares slope error between predictions and experiments. The result of the fit indicated that terms not associated with bias flow required a greater degree of correction than the terms associated with the bias flow. This model improved agreement with experiments by nearly 15% for the low percent open area (5%) samples when compared to the unfitted model. The fitted model and the unfitted model performed equally well for the higher percent open area (10% and 15%). / Ph. D.