In this work, we study the coupled dispersion characteristics of three distinct structural-acoustic waveguides, namely: -(1) a two-dimensional waveguide, (2) a fluid-filled circular cylindrical shell and (3)a fluid-filledelliptic cylindrical shell. Our primary interest is in finding coupled wavenumbers as functions of the fluid-structure coupling parameter(µ). Using the asymptotic solution methodology, we find the coupled wavenumbers as perturbations over the uncoupled wavenumbers of the component systems (the structure and the fluid). The asymptotic method provides us with analytical expressions of the coupled wavenumbers for small and large values of µ. The dispersion curves obtained from these extreme values of µ help in predicting the nature of the continuous transition of the wavenumber branches over the entire range of µ. Since the coupled wavenumbers are obtained as perturbations over the uncoupled wavenumbers, the perturbation term characterizes the effect of one medium over the other in terms of additional mass or stiffness. As is common in asymptotic methods, a particular form of the asymptotic expansion remains valid over a certain frequency range only. Hence, different scalings of the asymptotic parameter are used for different frequency ranges. In this regard, the method adopted uses principles of Matched Asymptotic Expansion (MAE). As mentioned above, we begin the study with a two-dimensional structural acoustic waveguide. Depending on the boundary condition at the top-edge of the fluid-layer (rigid or pressure-release), two cases are separately analyzed. In both these cases, only a single perturbation parameter (µ) is used. This is followed by the study of the axisymmetric mode vibration of a fluid-filled circular cylindrical shell. Here, in addition to , we include the Poisson’s ratio as another asymptotic parameter. The next problem studied is the beam mode (n =1)vibration of the same fluid-filled circular cylindrical shell. Here, the frequency is used as an asymptotic parameter (in addition to ) and the derivations proceed in two separate parts, one for the high frequency and the other for the low frequency. Having completed the n = 0 and n = 1 modes of the cylindrical shell, the higher order shell modes are studied using the simpler shallow shell theory. For the final system, viz., the elliptic cylindrical shell, another asymptotic parameter in the form of the eccentricity of the cross-section is used. Having derived the analytical expressions for the coupled wavenumbers and obtained the dispersion curves, a unified behavior of structural-acoustic systems is found to emerge. In all these systems, for small , the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-walled acoustic duct. The measure of closeness is quantified by . As µ increases, these wavenumber branches get shifted continuously till for large µ, the coupled wavenumber branches are better identified as perturbations to the wavenumbers of the pressure-release acoustic duct. At the coincidence region, the coupled structural wavenumber branch transits to the coupled acoustic wavenumber branchand vice-versa. As a result, at coincidence frequencies, while the uncoupled wavenumber branches intersect, due to the coupling, there is no longer an intersection. These common characteristics are shared amongst all the systems despite the difference in geometries. This suggests that the above discussed features capture the essential physics of sound-structure coupling in waveguides.This workthus presents a novel unified view-point to the topic. Along the way, some additional novel studies are conducted which do contribute to the completeness of the work. The free wavenumbers determined from the asymptotic expressions are usedto calculate the forced response of the two-dimensional waveguide due to a δ forcing. Using this analysis, we are able to come up with a novel explanation of the observation that with coupling the dispersion curves cannot intersect. Additionally, the effect of bulk flow in the acoustic fluid is also comprehensively studied for the easier case of the two-dimensional waveguide. Further, the well-known universal dispersion relation for the higher order circumferential modes of the in vacuo circular cylindrical shell is re-derived using a simpler method.

Underwater acoustic pressure transducers measure pressure fluctuations, a scalar parameter of the acoustic field. Acoustic vector sensors contain an omnidirectional pressure transducer (omni) and also bi- or tri-axial sensing elements that respond to either the particle velocity or pressure gradient of the acoustic field; which are vector quantities. The amplitude of the signal output of each directional channel of a vector sensor is proportional to the orientation relative to the direction of acoustic pressure propagation. The ratio of the signal amplitudes between two directional channels and the cross-spectra between the vector sensor omni and directional channels enable one to estimate the bearing to the source from a single point measurement. In order to accurately estimate the bearing across the usable frequency band of the vector sensor, the complex sensitivities of the omni and directional channels must be known. Since there is no standard directional reference transducer for a comparative calibration, the calibration must be performed in an acoustic field with a known relationship between the acoustic pressure and the acoustic particle velocity. Free-field calibrations are advantageous because this relationship is known for both planar and spherical wave fronts. However, reflections from waveguide boundaries present a practical limitation for free-field calibrations, especially at low frequencies. An alternative approach is to perform calibration measurements in a standing-wave field, where the relationship between pressure and particle velocity is also known. The calibration facility described in this thesis is composed of a laboratory-based, vertically-oriented, water-filled, elastic-walled waveguide with a piston velocity source at the bottom end and a pressure release boundary condition at the air/water interface at the top end. Some of the challenges of calibrating vector sensors in such an apparatus are discussed, including designing the waveguide to mitigate dispersion, mechanically isolating the apparatus from floor vibrations, understanding the impact of waveguide structural resonances on the acoustic field, and developing the calibration algorithms. Data from waveguide characterization experiments and calibration measurements are presented along with engineering drawings and calibration software. / text

Planar and cylindrical waveguides with linear cladding and a core with real, field dependent permittivity are considered, in particular even and odd modes are investigated.Assuming a plane wave with TE-polarization, Maxwell´s equations for the electric field lead to a nonlinear differential equation whose solution is approximated by means of a Green s function and an iteration method. Referring to a photorefractive permittivity with external field, the approximate solution is compared with the numerical solution; furthermore, the amplitude of even modes in the planar waveguide is compared with the analytically determined amplitude. In both cases, the agreement is satisfactory.The conditions of convergence of the iteration are investigated for a photorefractive permittivity with external field. It is shown that they are fulfilled for suitable choice of the width of the waveguide and the propagation constant. By means of the iteration method, the change of the linear dispersion relation due to the field dependent permittivity is described.The ratio of the power flow in the core to the total power flow is linearized in order to investigate the influence of weak nonlinearity.

[pt] Muitos dispositivos e estruturas empregados para guiar ondas eletromagnéticas apresentam conformidade cilíndrica. Aplicações sensíveis de engenharia de micro-ondas e de dispositivos ópticos integrados empregam, muitas vezes, materiais não homogêneos, anisotrópicos e dissipativos, de modo que a pesquisa por modelos computacionais robustos e acurados é um tópico de notável interesse para a Engenharia Elétrica. Este trabalho apresenta uma técnica semianalítica para resolver problemas de valor de contorno associados a guias de onda cilíndricos, anisotrópicos e não homogêneos. Nossa metodologia permite modelar estruturas com camadas radiais, com anisotropia uniaxial, e com perdas. A solução proposta parte das equações de Maxwell para campos harmônicos no tempo, e emprega uma expansão modal em termos da série de Bessel-Fourier. Os autovalores associados ao problema são obtidos por meio do método do winding number, em que diversas abordagens para o cálculo das integrais de caminho no plano complexo são exploradas. Para analisar junções entre guias de ondas estratificados, empregamos a técnica de casamento de modos baseada na conservação da Reação dos campos. Nossa formulação é capaz de avaliar os efeitos da excitação e do acoplamento entre modos puros (TM, TE, e TEM) em guias de ondas homogêneos, bem como dos modos híbridos em estruturas complexas. Uma série de resultados numéricos são apresentados e mostram a capacidade da metodologia desenvolvida nesta pesquisa para caracterizar corretamente estruturas cilíndricas compostas por meios complexos (não homogêneos, anisotrópicos e dissipativos) de forma robusta e computacionalmente eficiente se comparado com outras técnicas convencionais de eletromagnetismo computacional. / [en] Many devices and structures used to guide electromagnetic waves are conformal with the cylindrical coordinates. Sensitive applications of microwave engineering and integrated optical devices often use non-homogeneous, anisotropic and dissipative materials, so that the research for robust and accurate computational models is a topic of remarkable interest for Electrical Engineering. This work presents a semi-analytical technique for solving boundary-value problems associated with cylindrical, anisotropic, and non-homogeneous waveguides. Our methodology allows us to model structures with radial layers, with uniaxial anisotropy, and with losses. The proposed solution starts from Maxwell s equations for time-harmonic electromagnetic fields and employs a modal expansion in terms of the Bessel-Fourier series. The eigenvalues associated with the problem are obtained using the winding number method, in which several approaches for calculating complex-plane contour integrals are explored in detail. In order to properly analyze the junctions between sections of stratified waveguides, we employ a mode-matching technique based on the conservation of the Reaction of the fields. Our formulation can handle the effects of excitation and coupling between pure modes (TM, TE, and TEM) in homogeneous waveguides, as well as hybrid modes in complex structures. A series of numerical results are presented and show the capacity of the methodology developed here to correctly characterize cylindrical structures composed of complex media (inhomogeneous, anisotropic, and dissipative) in a robust and computationally-efficient fashion if compared to other conventional computational electromagnetic techniques.