No / A numerical method for sound propagation of higher-order cross-sectional modes in a duct of arbitrary cross-section and boundary conditions with nonzero, complex acoustic admittance has been considered. This method assumes that the cross-section of the duct is uniform and that the duct is of a considerable length so that the longitudinal modes can be neglected. The problem is reduced to a two-dimensional (2D) finite element (FE) solution, from which a set of cross-sectional eigen-values and eigen-functions are determined. This result is used to obtain the modal frequencies, velocities and the attenuation coefficients. The 2D FE solution is then extended to three-dimensional via the normal mode decomposition technique. The numerical solution is validated against experimental data for sound propagation in a pipe with inner walls partially covered by coarse sand or granulated rubber. The values of the eigen-frequencies calculated from the proposed numerical model are validated against those predicted by the standard analytical solution for both a circular and rectangular pipe with rigid walls. It is shown that the considered numerical method is useful for predicting the sound pressure distribution, attenuation, and eigen-frequencies in a duct with acoustically nonrigid boundary conditions. The purpose of this work is to pave the way for the development of an efficient inverse problem solution for the remote characterization of the acoustic boundary conditions in natural and artificial waveguides.

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.

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.

No / New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.