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The present work explores the possibilities of adapting poro-elastic lightweight acoustic materials to specific applications. More explicitly, a design approach is presented where finite element based numerical simulations are combined with optimization techniques to improve the dynamic and acoustic properties of lightweight multilayered panels containing poro-elastic acoustic materials. The numerical models are based on Biot theory which uses equivalent fluid/solid models with macroscopic space averaged material properties to describe the physical behaviour of poro-elastic materials. To systematically identify and compare specific beneficial or unfavourable material properties, the numerical model is connected to a gradient based optimizer. As the macroscopic material parameters used in Biot theory are interrelated, they are not suitable to be used as independent design variables. Instead scaling laws are applied to connect macroscopic material properties to the underlying microscopic geometrical properties that may be altered independently. The design approach is also combined with a structural sandwich panel mass optimization, to examine possible ways to handle the, sometimes contradicting, structural and acoustic demands. By carefully balancing structural and acoustic components, synergetic rather than contradictive effects could be achieved, resulting in multifunctional panels; hopefully making additional acoustic treatment, which may otherwise undo major parts of the weight reduction, redundant. The results indicate a significant potential to improve the dynamic and acoustic properties of multilayered panels with a minimum of added weight and volume. The developed modelling techniques could also be implemented in future computer based design tools for lightweight vehicle panels. This would possibly enable efficient mass reduction while limiting or, perhaps, totally avoiding the negative impact on sound and vibration properties that is, otherwise, a common side effect of reducing weight, thus helping to achieve lighter and more energy efficient vehicles in the future. / <p>QC 20120815</p>

When sound waves propagate in a duct in the presence of turbulent flow, turbulent mixing can cause attenuation of the sound waves extra to that caused by the viscothermal effects. Experiments show that compared to the viscothermal effects, this turbulent absorption becomes the dominant contribution to the sound attenuation at sufficiently low frequencies. The mechanism of this turbulent absorption is attributed to the turbulent stress and the turbulent heat transfer acting on the coherent perturbations (including the sound waves) near the duct wall, i.e. sound-turbulence interaction. The purpose of the current investigation is to understand the mechanism of the sound-turbulence interaction in low-Mach-number internal flows by theoretical modeling and numerical simulations. The turbulence absorption can be modeled through perturbation turbulent Reynolds stresses and perturbation turbulent heat flux in the linearized perturbation equations. In this thesis, the linearized perturbation equations are reviewed, and different models for the turbulent absorption of the sound waves are investigated. A new non–equilibrium model for the perturbation turbulent Reynolds stress is also proposed. The proposed model is validated by comparing with experimental data from the literature, and with the data from Direct Numerical Simulations (DNS) of pulsating turbulent channel flow. Good agreement is observed. / <p>QC 20150526</p>

We present immersed discontinuous Galerkin finite element methods for one and two dimensional acoustic wave propagation problems in inhomogeneous media where elements are allowed to be cut by the material interface. The proposed methods use the standard discontinuous Galerkin finite element formulation with polynomial approximation on elements that contain one fluid while on interface elements containing more than one fluid they use specially-built piecewise polynomial shape functions that satisfy appropriate interface jump conditions. The finite element spaces on interface elements satisfy physical interface conditions from the acoustic problem in addition to extended conditions derived from the system of partial differential equations. Additional curl-free and consistency conditions are added to generate bilinear and biquadratic piecewise shape functions for two dimensional problems. We established the existence and uniqueness of one dimensional immersed finite element shape functions and existence of two dimensional bilinear immersed finite element shape functions for the velocity. The proposed methods are tested on one dimensional problems and are extended to two dimensional problems where the problem is defined on a domain split by an interface into two different media. Our methods exhibit optimal $O(h^{p+1})$ convergence rates for one and two dimensional problems. However it is observed that one of the proposed methods is not stable for two dimensional interface problems with high contrast media such as water/air. We performed an analysis to prove that our immersed Petrov-Galerkin method is stable for interface problems with high jumps across the interface. Local time-stepping and parallel algorithms are used to speed up computation. Several realistic interface problems such as ether/glycerol, water/methyl-alcohol and water/air with a circular interface are solved to show the stability and robustness of our methods. / Ph. D.

Leakage and blockage of oil and gas pipeline systems, water pipelines, pipe-work of process plants and other pipe networks can cause serious environmental, health and economic problems. There are a number of non-destructive testing (NDT) methods for detecting these defects in pipeline systems such as radiographic, ultrasonic, magnetic particle inspection, pressure transient and acoustic wave methods. In this study, the acoustic wave method and a modal frequency technique, which based on a roving mass method, are used. The aim of the thesis is to employ acoustic wave propagation based methods in conjunction with stationary wavelet transform (SWT) to identify leakage and blockage in pipe systems. Moreover, the research is also aimed at using the difference of modal frequencies of fluid-filled pipes with and without defects and a roving mass, and consequently, to develop a roving mass-based defect detection method for pipelines. In the study, the acoustic finite-element analysis (AFEA) method is employed to simulate acoustic wave propagation in small and large air-filled water-filled straight pipe and pipe networks with leakage and blockage but without flow. Computational fluid dynamics (CFD) analysis was also employed to simulate acoustic wave propagation in air-and water-filled pipes with flow, leakage and blockage. In addition, AFEA was used to predict the modal frequencies of air- and water-filled pipes with leakage and blockage in the presence of a roving mass that was traversed along the axis of the pipes. Experimental testing was conducted to validate some of the numerical results. Two major experiments were performed. The first set of experiments consisted of the measurement of acoustic wave propagation in a straight air-filled pipe with leakage and blockage. The second set of experiments concerned the measurement of acoustic wave propagation in an air-filled pipe network comprising straight pipe, elbows and T-piece and flange. The AFEA and CFD analysis of fluid-filled pipe can be used to simulate the acoustic wave propagation and acoustic wave reflectometry of a fluid-filled pipe with leakage and blockage of different sizes down to a small leakage size of 1mm diameter and a blockage depth of 1.2mm in a pipe. Similarly, the AFEA method of a static fluid-filled pipe can be used to simulate acoustic wave modal frequency analysis of a fluid-filled pipe with leakage and blockage of different sizes down to a leakage of 1mm diameter and a blockage depth of 1.2mm. Moreover, the measured signal of acoustic wave propagation in an air-filled can be successfully decomposed and de-noised using the SWT method to identify and locate leakages of different sizes down to 5mm diameter, and small blockage depth of 1.2mm. Also, the SWT approximation coefficient, detail and de-noised detail coefficient curves of an air-filled pipe with leakage and blockage and a roving mass give leakage and blockage indications that can be used to identify, locate and estimate the size of leakage and blockage in a pipe.

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.

By projecting observed microseismic data backward in time to when fracturing occurred, it is possible to locate the fracture events in space, assuming a correct velocity model. In order to achieve this task in near real-time, a robust computational system to handle backward propagation, or Reverse Time Migration (RTM), is required. We can then test many different velocity models for each run of the RTM. We investigate the use of a Graphics Processing Unit (GPU) based system using Compute Unified Device Architecture for C (CUDA-C) as the programming language. Our preliminary results show a large improvement in run-time over conventional programming methods based on conventional Central Processing Unit (CPU) computing with Fortran. Considerable room for improvement still remains. / text

This thesis endeavors towards developing various concepts employed in analysis and design of acoustic filters for varied applications ranging from combination mufflers for automobiles to complex networks of gas carrying ducts to multiply connected complex automotive silencing devices to the noise control coatings for underwater applications. A two-dimensional wave modeling approach has been proposed to evaluate sound attenuation characteristics of dissipative mufflers of finite length with/without extended inlet and outlet tubes including very large mufflers. The correctness of the method has been validated through comparison with experimental results from literature. Two other frequently used approximate schemes have been discussed briefly with reference to the available literature. These three approaches have then been weighed against each other to show the effectiveness and limitations of each one. A thorough comparison study has been performed to investigate each one’s extent of applicability. A parametric study with different parameters suggests some useful design guidelines that can be put to use while designing such mufflers. Benefits and drawbacks of reactive and dissipative mufflers have been discussed with an intention of striking a compromise between them to achieve a better transmission quality over a broad frequency range. This has been accomplished by combining these two types of mufflers/filters explicitly. These combination mufflers are analyzed using a transfer matrix based approach by extending the aforesaid concept of two-dimensional wave modeling for finite dissipative ducts. The present approach has been used to analyze axi-symmetric circular lined plenum chambers also. The effectiveness of the bulk reaction assumption to model absorptive lining is illustrated. A parametric study has been carried out to investigate the effects of different thicknesses and placements of the absorptive lining. The contributions of reflective and absorptive portion of the combination mufflerto overall attenuation performance have been investigated from the designer’s point of view A generalized algorithm has been developed for studying the plane sound wave propa- gation in a system of interconnected rigid-walled acoustic filter elements. Interconnection between various elements is represented by a connectivity matrix. Equations of volume velocity continuity and pressure equilibrium at the interconnections are generated using this connectivity matrix and are solved using the Gauss-Jordan elimination scheme to get the overall transfer matrix of the system. The algorithm used for generalized labeling of the network and computation of Transmission Loss has also been discussed. The algorithm has been applied to investigate a multiply connected automobile mufflers as a network of acoustic elements which guides the way to a specialized application discussed next. Results for some configurations have been compared with those from the FEM analysis and experiments. A parametric study with respect to some geometric variables is carried out. The acoustical similarity between apparently different networks is discussed. The approach is flexible to incorporate any other acoustic elements, provided the acoustic variables at the junctions of the element can be related by a transfer matrix a priori. Commercial automotive mufflers are often too complex to be broken into a cascade of one dimensional elements with predetermined transfer matrices. The one dimensional (1-D) scheme presented here is based on an algorithm that uses user friendly visual volume elements to generate the system equations which are then solved using a Gauss-Jordan elimination scheme to derive the overall transfer matrix of the muffler. This work attempts and succeeds to a great extent in exploiting the speed of the one dimensional analysis with the flexibility, generality and user friendliness of three dimensional analysis using geometric modeling. A code based on the developed algorithm has been employed to demonstrate the generality of the proposed method in analyzing commercial muffers by considering three very diverse classes of mufflers with different kinds of combinations of reactive, perforated and absorptive elements. Though the examples presented in the thesis are not very complex for they are meant to be just representative cases of certain classes of mufflers, yet the algorithm can handle a large domain of commercial mufflers of high degree of complexity. Results from the present algorithm have been validated through comparisons with both the analytical and the more general, three-dimensional FEM based results. The forte of the proposed method is its power to construct the system matrix consistent with the boundary conditions from the geometrical model to evaluate the four pole parameters of the entire muffer and thence its transmission loss,etc. Thus, the algorithm can be used in conjunction with the transfer matrix based muffler programs to analyze the entire exhaust system of an automobile. A different kind of acoustic filter than the above mentioned cases is then taken up for investigation. These refer to the specialized underwater acoustic filters laid as linings on submerged bodies. These kind of underwater noise control linings have three different types of objectives, namely, Echo Reduction, Transmission Reduction (TL maximization) and a combination thereof. These coatings have been shown to be behaving very differently with different shape, size and number of air channels present in the layer. In this regard, a finite element model based methodology has been followed. An hybrid type finite element based on the Pian and Tong formulation has been modified and used so as to make the computational efforts less demanding as compared to the original one. The developed finite element has been shown to be immune to the difficulties that arise due to the near incompressible characteristics of the viscoelastic materials used and the high distortion of the elements of the FE mesh. The adequacy of this formulation has been shown by comparing its results with the analytical, FE based, and experimental results. Then, this methodology has been used to analyze and generate design curves to control various geometrical parameters for proper designing of these linings. Different unit cell representations for different types of distributions of air cavities on the linings have been discussed. Four different types of layers have been introduced and analyzed to address different objectives mentioned above. They have been termed as the Anechoic layer, Insulation layer and Combination Layer of coupled and decoupled type in this thesis. The first two layers have been designed to achieve very dissimilar characteristics and the next two layers have been designed to balance their disparities. A thorough parametric study has been carried out on the geometrical parameters of all the layers to come up with the design guidelines. For anechoic and the insulation layers, different distributions have been analyzed with different unit cell geometries and their usability in specific situations has been outlined. Effect of static pressure has also been studied by using an approximate finite element method. This method can be used to simulate deep-sea testing environment.

Boundary shape optimization is a technique to search for an optimal shape by modifying the boundary of a device with a pre-specified topology. We consider boundary shape optimization of acoustic horns in loudspeakers and brass wind instruments. A horn is an interfacial device, situated between a source, such as a waveguide or a transducer, and surrounding space. Horns are used to control both the transmission properties from the source and the spatial power distribution in the far-field (directivity patterns). Transmission and directivity properties of a horn are sensitive to the shape of the horn flare. By changing the horn flare we design transmission efficient horns. However, it is difficult to achieve both controllability of directivity patterns and high transmission efficiency by using only changes in the horn flare. Therefore we use simultaneous shape and so-called topology optimization to design a horn/acoustic-lens combination to achieve high transmission efficiency and even directivity. We also design transmission efficient interfacial devices without imposing an upper constraint on the mouth diameter. The results demonstrate that there appears to be a natural limit on the optimal mouth diameter. We optimize brasswind instruments with respect to its intonation properties. The instrument is modeled using a hybrid method between a one-dimensional transmission line analogy for the slowly flaring part of the instrument, and a finite element model for the rapidly flaring part. An experimental study is carried out to verify the transmission properties of optimized horn. We produce a prototype of an optimized horn and then measure the input impedance of the horn. The measured values agree reasonably well with the predicted optimal values. The finite element method and the boundary element method are used as discretization methods in the thesis. Gradient-based optimization methods are used for optimization, in which the gradients are supplied by the adjoint methods.

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.