Commercial aircraft are subject to noise regulations imposed by the Federal Aviation Administration. Currently, the FAA limits overland flight of supersonic airplanes due to the negative effect of the sonic boom on communities. The annoyance produced by the impulsive signature of sonic booms, particularly indoors, cannot exceed that of the broadband, low-overpressure noise produced by subsonic airplanes for the restriction to be lifted. Therefore, the ability to understand and accurately reproduce the acoustic response of a sonic boom is important for psychoacoustic classification of their tolerability within residences. This thesis presents and interprets results of the propagation and transmission of simulated sonic booms incident on wood-framed structures. The testing environment, sonic boom simulation method, and associated instrumentation are described. The effects of the traveling blast on the structure are investigated through pressure loading and structural response measurements. The ensuing interior acoustic responses for several different configurations are presented, including the effects of room cavity interaction and exposure of the room cavities to the traveling wave through an open door. Calculated transfer functions between the interior acoustic response and the free-field incident wave are computed to assess the extent to which wood-framed buildings transmit energy to their cavities. In all cases tested, significant transmission of the sonic boom's low frequency content into the structures was apparent through direct apertures and the excitation of structural components. The data show that sonic booms provide significant excitation of structural and acoustic modes that drives the interior acoustic response in residential structures. / Master of Science

ITC/USA 2012 Conference Proceedings / The Forty-Eighth Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2012 / Town and Country Resort & Convention Center, San Diego, California / The Western Aeronautical Test Range of the National Aeronautics and Space Administration's Dryden Flight Research Center needed to address the aging software and hardware of its current situational awareness display application, the Global Real-Time Interactive Map (GRIM). GRIM was initially developed in the late 1980s and executes on older PC architectures using a Linux operating system that is no longer supported. Additionally, the software is difficult to maintain due to its complexity and loss of developer knowledge. It was decided that a replacement application must be developed or acquired in the near future. The replacement must provide the functionality of the original system, the ability to monitor test flight vehicles in real-time, and add improvements such as high resolution imagery and true 3-dimensional capability. This paper will discuss the process of determining the best approach to replace GRIM, and the functionality and capabilities of the first release of the Positional Awareness Map 3D.

The thesis develops the acoustic theory of the propagation of the shook waves produced by an aircraft in supersonic flight through an atmosphere in which the speed of sound decreases linearly with altitude. The problem is first studied in terms of the geometry of the rays along which the shock wave travels away from its point of origin and into the surrounding atmosphere. The equation of the rays is derived and certain important properties of the rays are discussed. It is shown how these results lead to a systematic graphical procedure for determining the location of the shock wave of a maneuvering aircraft. The theory is then considered in terms of the geometry of the "wave fronts" which represent the instantaneous positions of the individual disturbances created along the flight path. The shape of a wave front and its growth with time are determined. From this the equations for the envelope of a one-parameter family of wave fronts are obtained. The envelope equations are solved in parametric form and several examples are worked out which show some effects of flight maneuvers upon shock wave propagation. / M.S.

Sonic boom annoyance is an important technical showstopper for commercial supersonic aircraft operations. It has been proposed that aircraft can be shaped to alleviate sonic boom. Choosing the right aircraft shape reflecting the design requirements is a fundamental and most important step that is usually over simplified in the conceptual stages of design by resorting to a qualitative selection of a baseline configuration based on historical designs and designers perspective. Final aircraft designs are attempted by minor shape modifications to this baseline configuration. This procedure may not yield large improvements in the objectives, especially when the baseline is chosen without a rigorous analysis procedure. Traditional analyses and implementations tend to have a complex algorithmic flow, tight coupling between tools used and computational limitations. Some of these shortcomings are overcome in this study and a diverse mix of tools is seamlessly integrated to provide a simple, yet powerful and automatic procedure for sonic boom minimization. A shape optimization procedure for supersonic aircraft design using better geometry generation and improved analysis tools has been successfully demonstrated. The geometry engine provides dynamic reconfiguration and efficient manipulation of various components to yield unstructured watertight geometries. The architecture supports an assimilation of different components and allows configuration changes to be made quickly and efficiently because changes are localized to each component. It also enables an automatic way to combine linear and non-linear analyses tools. It has been shown in this study that varying atmospheric conditions could have a huge impact on the sonic boom annoyance metrics and a quick way of obtaining probability estimates of relevant metrics was demonstrated. The well-accepted theoretical sonic boom minimization equations are generalized to a new form and the relevant equations are derived to yield increased flexibility in aircraft design process. Optimum aircraft shapes are obtained in the conceptual design stages weighing in various conflicting objectives. The unique shape optimization procedure in conjunction with parallel genetic algorithms improves the computational time of the analysis and allows quick exploration of the vast design space. The salient features of the final designs are explained. Future research recommendations are made.

The Utah State University Aerolab developed and tested a set of tools for rapid prediction of the loudness of a sonic boom generated by supersonic transport aircraft. This work supported a larger effort led by Texas A&M to investigate the use of adaptive aerostructures in lowering sonic boom loudness at off design conditions. Successful completion of this effort will improve the feasibility of supersonic commercial transport over land. Funding was provided by a NASA University Leadership Initiative grant to several universities, including Utah State University, as well as industry partners to complete this work over a five year period. The work presented in this thesis was done over the first year of the grant. The Aerolab team was specifically tasked with developing a set of tools for rapidly predicting the sonic boom loudness of supersonic aircraft. Specifically, this work included an assessment of the existing analysis tools available followed by the planning, development, and testing of a framework of tools for performing the needed calculations. Results of the framework were compared against high fidelity solutions available from the 2017 AIAA Sonic Boom Prediction Workshop. These comparisons revealed that panel methods perform well for simple geometries. However, localized errors appear when modeling more complex geometries that reduce the accuracy of the predicted sonic boom loudness. It was found that these localized errors were a consequence of the inherent assumptions built into panel methods. Consequently, in future work, it may be necessary to develop techniques for combining the results of panel methods with higher fidelity methods or to revisit the panel method formulation.

In this thesis, an output-only experimental modal testing and analysis technique known as the Natural Excitation Technique (NExT) is examined for use with large residential structures and interior cavities. The technique which assumes a random, stationary input causing the response data is reviewed and extended for the first time to include the assumption of an impulse input. This technique is examined with respect to the experimental modal analysis of single and two room residential structures. Each structure is first tested using conventional modal testing methods. Then, NExT is applied using each structure's response to a simulated sonic boom, an impulsive input. The results of these analyses along with the results obtained from a finite element model are compared. Then, the interior cavities enclosed by the residential structures are examined using NExT. Therefore, this thesis also demonstrates the successful use of NExT on acoustic systems for the first time. Three configurations of the interconnected cavities enclosed by the two room structure are considered to study physical phenomena. Both interior pressure response to random, stationary inputs and the sonic boom response are used with NExT to determine modal properties. The results of these analyses are compared to a theoretical analysis. Advantages to using NExT with both the response to a random, stationary input and an impulsive input are demonstrated for structural and acoustic systems. / Master of Science

Pas de résumé / Propagation of nonlinear acoustic waves in inhomogeneous media is an important problem inmany research domains of modern theoretical and applied acoustics. For example, studies onpropagation of high amplitude N-waves in turbulent atmosphere are relevant to the sonic boomproblem which involves high interest due to development of new civil supersonic aircrafts. Inrelation to sonic boom problem, many studies on spark-generated N-wave propagation through aturbulent layer were carried out in model laboratory-scale experiments which are more controlledand reproducible than field measurements. Propagation of high intensity focused ultrasound intissue (HIFU) is intensively studied for medical applications. HIFU is a basis of new surgicaldevices for noninvasive thermal and mechanical ablation of tumors.In this thesis, the problem of characterization of high amplitude N-waves generated in air byan electric spark was studied using combined acoustical and optical methods. The fine structureof shocks was deduced from the shadowgraphy images with a resolution that cannot be obtainedusing condenser microphones. It was shown that the combination of optical and acoustical methodsallows complete characterization of the N-waves.N-wave propagation through a layer of thermal turbulence was further studied in a laboratoryexperiment. The evolution of statistical distributions and average values of the most importantN-wave parameters was investigated at different propagation distances. Experimental results werecompared to data obtained in another experiment known in literature, where N-wave was propagatedthrough kinematic turbulence. It was shown that in the case of almost the same widths ofthe turbulent layers, values of the characteristic scales and rms of refractive index fluctuations, thekinematic turbulence leads to stronger distortions of the peak pressure and the shock rise time ofthe N-wave and to 2-3 greater probabilities to observe intense focusing in caustics.Effects of nonlinear propagation and random focusing on the statistics of N-wave amplitudewere studied theoretically using the KZK equation and the phase screen model. The phase screenwas characterized by the correlation length and the refraction length – the distance where firstcaustics occur. Probability distributions, mean values and standard deviations of the N-wave peakpressure were obtained from the numerical solutions and were presented as functions of the propagationdistance and the nonlinear length. Statistical results from the KZK model were comparedwith analytical predictions of the nonlinear geometrical acoustics approach (NGA). It was shown,that NGA approach is valid only up to the distance of one third of refraction length of the screen.Strong nonlinear effects were shown to suppress amplitude fluctuations. The effect of the scale ofinhomogeneities on amplitude statistics was also investigated.The problem of focusing of ultrasound beam through inhomogeneous medium is importantfor medical diagnostics and nondestructive testing problems. The inhomogeneities of biologicaltissue or of industrial materials can destroy beam focusing. In the thesis, distortions of a weaklynonlinear diagnostic beam focused through a phase layer of special configuration were consideredexperimentally and theoretically. Feasibility of selective destruction of focusing of differentharmonics in the beam was predicted in the modeling and confirmed in experiment.The most modern HIFU devices rely on using two-dimensional multi-element phased arrayswith elements randomly distributed over a segment of a spherical surface. Numerical experimentis an important tool to characterize pressure fields created by HIFU radiators. Intensity levels atthe focus of HIFU radiators can reach several tens of thousands of W/cm2, causing nonlinearpropagation effects and formation of shocks [...]

Recent progresses by the aircraft industry in the development of a quieter supersonic transport have opened the possibility of overland supersonic flights, which are currently banned by aviation authorities in most countries. For the ban to be lifted, the sonic booms the aircraft generate at supersonic speed must be acceptable from a human-perception point of view, in particular inside buildings. The problem of the transmission of sonic booms inside buildings can be divided in several aspects such as the external pressure loading, structure vibration, and interior acoustic response. Past investigations on this problem have tackled all these aspects but were limited to simple structures and often did not account for the coupled fluid-structure interaction. A more comprehensive work that includes all the effects of sonic booms to ultimately predict the noise exposure inside realistic building structures, e.g. residential houses, has never been reported. Thus far, these effects could only be investigated experimentally, e.g. flight tests. In this research, a numerical model and a computer code are developed within the above context to predict the vibro-acoustic response of simplified building structures exposed to sonic booms, at low frequency. The model is applicable to structures with multiple rectangular cavities, isolated or interconnected with openings. The response of the fluid-structure system, including their fully coupled interaction, is computed in the time domain using a modal-decomposition approach for both the structural and acoustic systems. In the dynamic equations, the structural displacement is expressed in terms of summations over the "in vacuo" normal modes of vibration. The interior pressure is expressed in terms of summations over the acoustic modes of the rooms with perfectly reflecting surfaces (hard walls). This approach is simple to implement and computationally efficient at low frequency, when the modal density is relatively low. The numerical model is designed specifically for this application and includes several novel formulations. Firstly, a new shell finite-element is derived to model the structural components typically used in building construction that have orthotropic characteristics such as plaster-wood walls, floors, and siding panels. The constitutive matrix for these types of components is formulated using simple analytical expressions based on the orthotropic constants of an equivalent orthotropic plate. This approach is computationally efficient since there is no need to model all the individual subcomponents of the assembly (studs, sheathing, etc.) and their interconnections. Secondly, a dedicated finite-element module is developed that implements the new shell element for orthotropic components as well as a conventional shell element for isotropic components, e.g. window panels and doors. The finite element module computes the "in vacuo" structural modes of vibration. The modes and external pressure distribution are then used to compute modal loads. This dedicated finite-element module has the main advantage of overcoming the need, and subsequent complications, for using a large commercial finite-element program. Lastly, a novel formulation is developed for the fully coupled fluid-structure model to handle room openings and compute the acoustic response of interconnected rooms. The formulation is based on the Helmholtz resonator approach and is applicable to the very low frequency-range, when the acoustic wavelength is much larger than the opening dimensions. Experimental validation of the numerical model and computer code is presented for three test cases of increasing complexity. The first test structure consists of a single plaster-wood wall backed by a rigid rectangular enclosure. The structure is excited by sonic booms generated with a speaker. The second test structure is a single room made of plaster-wood walls with two double-panel windows and a door. The third test structure consists of the first room to which a second room with a large window assembly was added. Several door configurations of the structure are tested to validate the formulation for room openings. This latter case is the most realistic one as it involves the interaction of several structural components with several interior cavities. For the last two test cases, sonic booms with realistic durations and amplitudes were generated using an explosive technique. Numerical predictions are compared to the experimental data for the three test cases and show a good overall agreement. Finally, results from a parametric study are presented for the case of the single wall backed by a rigid enclosure. The effects of sonic-boom shape, e.g. rise time and duration, and effects of the structure geometry on the fluid-structure response to sonic booms are investigated. / Ph. D.

Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic Cauchy problems are typically ill-posed, i.e., there may not be a solution for some Cauchy data, and even if a solution exists uniquely, it may not depend continuously on the Cauchy data. The ill-posedness causes numerical instability and makes the classical numerical methods inappropriate to solve such problems. For Cauchy problems, the research on uniqueness, stability, and efficient numerical methods are of significant interest to mathematicians. The main focus of this thesis is to develop numerical techniques for elliptic Cauchy problems. Elliptic Cauchy problems can be approached as data completion problems, i.e., from over-specified Cauchy data on an accessible part of the boundary, one can try to recover missing data on the inaccessible part of the boundary. Then, the Cauchy problems can be solved by finding a so-lution to a well-posed boundary value problem for which the recovered data constitute a boundary condition on the inaccessible part of the boundary. In this thesis, we use natural linearization approach to transform the linear Cauchy problem into a problem of solving a linear operator equation. We consider this operator in a weaker image space H−1, which differs from the previous works where the image space of the operator is usually considered as L2 . The lower smoothness of the image space will make a problem a bit more ill-posed. But under such settings, we can prove the compactness of the considered operator. At the same time, it allows a relaxation of the assumption concerning noise. The numerical methods that can cope with these ill-posed operator equations are the so called regularization methods. One prominent example of such regularization methods is Tikhonov regularization which is frequently used in practice. Tikhonov regularization can be considered as a least-squares tracking of data with a regularization term. In this thesis we discuss a possibility to improve the reconstruction accuracy of the Tikhonov regularization method by using an iterative modification of Tikhonov regularization. With this iterated Tikhonov regularization the effect of the penalty term fades away as iterations go on. In the application of iterated Tikhonov regularization, we find that for severely ill-posed problems such as elliptic Cauchy problems, discretization has such a powerful influence on the accuracy of the regularized solution that only with some reasonable discretization level, desirable accuracy can be achieved. Thus, regularization by projection method which is commonly known as self-regularization is also considered in this thesis. With this method, the regularization is achieved only by discretization along with an appropriate choice of discretization level. For all regularization methods, the choice of an appropriate regularization parameter is a crucial issue. For this purpose, we propose the balancing principle which is a recently introduced powerful technique for the choice of the regularization parameter. While applying this principle, a balance between the components related to the convergence rate and stability in the accuracy estimates has to be made. The main advantage of the balancing principle is that it can work in an adaptive way to obtain an appropriate value of the regularization parameter, and it does not use any quantitative knowledge of convergence rate or stability. The accuracy provided by this adaptive strategy is worse only by a constant factor than one could achieve in the case of known stability and convergence rates. We apply the balancing principle in both iterated Tikhonov regularization and self-regularization methods to choose the proper regularization parameters. In the thesis, we also investigate numerical techniques based on iterative Tikhonov regular-ization for nonlinear elliptic Cauchy problems. We consider two types of problems. In the first kind, the nonlinear problem can be transformed to a linear problem while in the second kind, linearization of the nonlinear problem is not possible, and for this we propose a special iterative method which differs from methods such as Landweber iteration and Newton-type method which are usually based on the calculation of the Frech´et derivative or adjoint of the equation. Abundant examples are presented in the thesis, which illustrate the performance of the pro-posed regularization methods as well as the balancing principle. At the same time, these examples can be viewed as a support for the theoretical results achieved in this thesis. In the end of this thesis, we describe the sonic boom problem, where we first encountered the ill-posed nonlinear Cauchy problem. This is a very difficult problem and hence we took this problem to provide a motivation for the model problems. These model problems are discussed one by one in the thesis in the increasing order of difficulty, ending with the nonlinear problems in Chapter 5. The main results of the dissertation are communicated in the article [35].

Ce travail porte sur le développement de méthodes numériques innovantes pour la conception aéro-acoustique optimale de forme des configurations supersoniques. Ce manuscrit présente tout d'abord l'analyse et le développement des approches numériques pour la prévision du bang sonique . Le couplage du calcul CFD tridimensionnel en champ proche prenant en compte la décomposition multipolaire de Fourier et la propagation atmosphérique basée sur un algorithme de tracé de rayons est amélioré par l’intégration d'un processus automatique d' adaptation anisotrope de maillage. La deuxième partie de ce travail se concentre sur l’élaboration et l'application des techniques de conception pour l'optimisation d'une configuration aile-fuselage supersonique. Un module de conception inverse, AIDA , fournit à partir d'une signature acoustique cible au sol à faible bang sonique la géométrie de la configuration correspondante. Pour améliorer a la fois les performances acoustique et aérodynamique, des techniques d'optimisation directes de forme sont utilisées pour résoudre des problèmes d'optimisation mono et multi- disciplinaires et une analyse détaillée est réalisée. Des stratégies innovantes basées sur la coopération et les jeux compétitifs sont enfin appliquées au problème d'optimisation multidisciplinaire offrant une alternative aux algorithmes traditionnels MDO . L’hybridation de ces deux stratégies ouvre la voie a une nouvelle façon d'explorer le front de Pareto de manière efficace. Celle-ci est mise en application sur un cas pratique. / This work addresses the development of original numerical methods for the aero-acoustic optimal shape design of supersonic configurations. The first axis of the present research is the enhancement of numerical approaches for the prediction of sonic boom. The three dimensional CFD near-field prediction matched using a multipole decomposition approach coupled with atmospheric propagation using on a ray-tracing algorithm is improved by the integration of an automated anisotropic mesh adaptation process. The second part of this work focuses on the formulation and development of design techniques for the optimization of a supersonic wing-body configuration. An inverse design module, AIDA, is able to determine an equivalent configuration provided a target shaped signature at ground level corresponding to a low-boom profile. In order to improve both the aerodynamic and the acoustic performance, direct shape optimization techniques are used to solve single and multi-disciplinary optimization problems and a detailed analysis is carried out. At last, innovative strategies based on cooperation and competitive games are then applied to the multi-disciplinary optimization problem providing an alternative to traditional MDO algorithms. Hybridizing the two strategies opens a new efficient way to explore the Pareto front and this is shown on a practical case.