Thesis (Ph. D.)--University of Michigan, 1942. / "Reprinted from the Journal of the Acoustical society of America, vol. 14, no. 1 ... July, 1942."

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An innovative implementation of the skin concept for the reduction of the radiated sound power from a vibrating structure is proposed. The skin has a periodic structure and continuously covers a vibrating beam. Thus, this skin decouples the vibrating structure from the acoustic field by modifying the wavenumber spectrum of the radiating surface. First, structural acoustics and periodic structure theories are reviewed in order to predict how bending waves propagate along a periodic beam and how this beam radiates sound. These theories are then extended to the case of multi-layered structures in order to understand the behavior of a beam loaded with a periodic skin. In order to design the beam and skin structural periods, two different methods are used: Galois sequences and an optimization process using a real-valued genetic algorithm. Simulations are run for the case of periodic beams and beams coupled with periodic smart skins in both finite and infinite configurations. Results show that periodic beam can radiate less sound than equivalent uniform structures. Results also show the potential of periodic skin for application to the structural radiation problem for frequencies higher than approximately 100Hz with an approximately 10dB of radiated sound power attenuation. / Master of Science

<p>In the industry, all passenger vehicles are treated with damping materials to reduce structure-borne sound. Though these damping materials are effective to attenuate structure-borne sound, they have little or no effect on the air-borne sound transmission.The lack of effective predictive methods for assessing the acoustic effects due to added damping on complex industrial structures leads to excessive use of damping materials.Examples are found in the railway industry where sometimes the damping material applied per carriage is more than one ton. The objective of this thesis is to provide a better understanding of the application of these damping materials in particular when applied to lightweight sandwich panels.</p><p>As product development is carried out in a fast pace today, there is a strong need for validated prediction tools to assist in the design process. Sound transmission loss of sandwich plates with isotropic core materials can be accurately predicted by calculating the wave propagation in the structure. A modified wave propagation approach is used to predict the sound transmission loss of sandwich panels with honeycomb cores. The honeycomb panels are treated as being orthotropic and the wave numbers are calculated for the two principle directions. The orthotropic panel theory is used to predict the sound transmission loss of panels. Visco-elastic damping with a constraining layer is applied to these structures and the effect of these damping treatment on the sound transmission loss is studied. Measurements are performed to validate these predictions.</p><p>Sound radiated from vibrating structures is of great practical importance.The radiation loss factor represents damping associated with the radiation of sound as a result of the vibrating structure and can be a significant contribution for structures around the critical frequency and for composite structures that are very lightly damped. The influence of the radiation loss factor on the sound reduction index of such structures is also studied.</p> / QC 20100519 / ECO2-Multifunctional body Panels

This thesis describes the results of the experimental investigations into some new geometrical configurations in plate-like structures materialising one-dimensional (1D) acoustic black holes for flexural waves (wedges of power-law profile) and two-dimensional (2D) acoustic black holes for flexural waves (circular indentations of power-law profile). Such acoustic black holes allow the user to reduce the amplitudes of the vibration responses of plate-like structures to a maximum effect, while not increasing the mass of the structures. This thesis also suggests some new real world practical applications for this damping technique. Initially, the effects of geometrical and material imperfections on damping flexural vibrations in plates with attached wedges of power-law profile (1D black holes) were investigated, demonstrating that this method of damping is robust enough for practical applications. Then, damping of flexural vibrations in turbofan blades with trailing edges tapered according to a power-law profile has been investigated. In addition, experimental investigations into power-law profiled slots within plates have been also conducted. Another important configuration under investigation was that of circular indentations (pits) of power-law profile within the plate. In the case of quadratic or higher-order profiles, such indentations materialise 2D acoustic black holes for flexural waves. To increase the damping efficiency of power-law profiled indentations, the absorption area has been enlarged by increasing the size of the central hole in the pit, while keeping the edges sharp. The next step of investigation in this thesis was using multiple indentations of power-law profile (arrays of 2D black holes). It was shown that not only do multiple indentations of power-law profile provide substantial reduction in the damping of flexural vibrations, but also a substantial reduction in radiated sound power. The experimental results have been obtained also for a cylindrical plate incorporating a central hole of quadratic profile. They are compared to the results of numerical predictions, thus validating the results and the experimental technique. Investigations into the effects of indentations of power-law profile made in composite plates and panels and their subsequent inclusion into composite honeycomb sandwich panels are also reported. These indentations again act as 2D acoustic black holes for flexural waves and they effectively damp flexural vibrations within the panels. It was also demonstrated that these indentations can be enclosed in smooth surfaced panels and that no additional damping layer is required to induce the acoustic black hole effect in composite structures. In conclusion, it has been confirmed in this thesis that one and two-dimensional acoustic black holes represent an effective method of damping flexural vibrations and reducing the associated structure-borne sound. Furthermore, this thesis has shown that acoustic black holes can be efficiently employed in practical applications, such as trailing edges of jet engine fan blades, composite panels, and composite honeycomb sandwich structures.

It is difficult to predict the sound radiation from large factory roofs. The existing infinite panel theories of sound insulation are not sufficient when the sound radiates at grazing angles. It has been shown that the reason for the collapse of the theory is the well known result for the radiation efficiency. This research will present a simple analytic strip theory, which agrees reasonably well with numerical calculations for a rectangular panel. Simple analytic strip theory has lead to the conclusion that it is mainly the length of the panel in the direction of radiation, rather than its width that is important in determining its radiation efficiency. The findings of the current research also indicated that apart from the effect due to coincidence, a panel was non-directional compared to an opening.

In the industry, all passenger vehicles are treated with damping materials to reduce structure-borne sound. Though these damping materials are effective to attenuate structure-borne sound, they have little or no effect on the air-borne sound transmission.The lack of effective predictive methods for assessing the acoustic effects due to added damping on complex industrial structures leads to excessive use of damping materials.Examples are found in the railway industry where sometimes the damping material applied per carriage is more than one ton. The objective of this thesis is to provide a better understanding of the application of these damping materials in particular when applied to lightweight sandwich panels. As product development is carried out in a fast pace today, there is a strong need for validated prediction tools to assist in the design process. Sound transmission loss of sandwich plates with isotropic core materials can be accurately predicted by calculating the wave propagation in the structure. A modified wave propagation approach is used to predict the sound transmission loss of sandwich panels with honeycomb cores. The honeycomb panels are treated as being orthotropic and the wave numbers are calculated for the two principle directions. The orthotropic panel theory is used to predict the sound transmission loss of panels. Visco-elastic damping with a constraining layer is applied to these structures and the effect of these damping treatment on the sound transmission loss is studied. Measurements are performed to validate these predictions. Sound radiated from vibrating structures is of great practical importance.The radiation loss factor represents damping associated with the radiation of sound as a result of the vibrating structure and can be a significant contribution for structures around the critical frequency and for composite structures that are very lightly damped. The influence of the radiation loss factor on the sound reduction index of such structures is also studied. / QC 20100519 / ECO2-Multifunctional body Panels

Sound radiation from an acoustic source typically exhibits directional behavior, as is the case for the human voice, musical instruments, and loudspeakers, to name just a few. The necessity of directional data for many applications, such as sound source modeling, microphone placement, room acoustical design, and auralization, motivates directivity measurements. However, these measurements require careful understanding and implementation to produce the most meaningful results. Accordingly, this dissertation addresses several topics relevant to directivity theory, measurement, processing, and application. It first expands and amends previously published concepts of an acoustic source center and demonstrates the close relationship between the center and a source's far-field directional response. This relationship subsequently leads to an acoustic centering method that improves source placements within directivity measurement arrays. The dissertation then addresses several measurement considerations, including the required numbers of sampling positions for directivity measurements, quadrature rules applicable to standardized dual-equiangular sampling schemes, and a source's far-field response from arbitrarily shaped microphone arrays. Selected directivity results for the human voice and musical instruments illustrate applications of the developed measurement theories for procuring high-resolution results over a sphere. Compiled voice and musical instrument directivities now appear in an open-source database for use in room acoustical modeling, microphone placements, and other applications. To better elucidate and help predict sound source radiation, this work proposes several theoretical models, including equivalent point-source models, low-frequency radiation from a radially vibrating cap set on a rigid spherical shell with a circular aperture, and radiation from a vibrating cap on a rigid sphere with imposed mode shapes. Finally, this dissertation presents two microphone placement methods for audio and other applications. The first method approximates the measurement of a source's sound power spectrum through a single-channel measurement; the second considers microphone placement for maximum perceived loudness. The work's various developments, results, and conclusions will assist researchers and practitioners in better evaluating, predicting, and applying sound source directivities for many uses.

A deterministic approach based on a modal expansion and modal receptance method has been developed to evaluate the airborne sound insulation of aircraft panels with stringer and ring frame attachments. Furthermore, this method was extended to predict the noise radiation of stiffening panel subjected to TBL excitation. This approach integrates with the fast and accurate methods in evaluating the modal excitation terms and modal radiation efficiency. Based on these advantages, the effects of the curvature, overpressure, stringers, ring frames, hydrodynamic coincidence, composite structures and structural dissipation on the acoustical properties of a typical aircraft panel are able to be investigated efficiently. Theoretic predictions were compared with laboratory measurements conducted on both model structures and aircraft panels. It was found that a small curvature may result in significant deterioration of the sound transmission loss at frequencies of interest. Unlike a flat uniform panel, the theoretical prediction for curved panels from the infinite model can not provide good agreement with the measurement close to and well below the ring frequency. However, in this frequency range, the finite model has been proved to be applicable For the large curved airplane panels studied here, it was found that the ring frames have little influence on sound transmission loss in the frequency range of interest. However the stringers may have considerable influence on sound transmission loss. The stringer improves this for a curved panel around the ring frequency, but it may result in a potential deterioration of the sound transmission loss above the ring frequency. In this study it is evident that the sound transmission loss of the composite skin attached with composite stringers is lower than that of the metallic panel attached with metallic stringers. At frequencies higher than the corresponding ring frequency of the curved panel, both experiment and theoretical prediction reveal that the overpressure at the concave side tends to reduce the sound transmission loss at the rate of about 0.5dB /10000 Pa. While at lower frequencies, say well below the ring frequency, the overpressure may increase or reduce sound transmission loss of a finite panel, depending on the shift of the resonant frequencies resulting from the overpressure. For TBL excitation, numerical investigation reveals that the panel with the ring frames behaves more like a sub-panel between two frames. Below 500Hz, the ring frames slightly enhance the sound radiation while dramatically increasing it around 1.3kHz. The TBL forcing field excites the same vibration lever for the panel with and without ring frame attachments, but the modes excited for the panel with ring frames radiate more sound. Unlike the ring frames, the stringers increase sound radiation below 1kHz. Above 1kHz, the sub-panels between two bays respond independently and the stringer effects is therefore not obvious. / <p>QC 20100908</p>

Vibrações estruturais constituem uma das principais fontes de ruído e de desconforto em diversas aplicações, tais como nos produtos das indústrias automotiva, aeroespacial e naval, que, em grande parte, são compostos por estruturas flexíveis semelhantes a placas. Ao mesmo tempo, a demanda crescente por aumento de eficiência energética e por redução de emissão de gases nocivos ao meio ambiente tem levado os fabricantes de todos os segmentos para a utilização de materiais cada vez mais leves. Um desafio importante relacionado ao uso dessas soluções diz respeito ao seu comportamento vibroacústico, já que estruturas leves tendem a transmitir e emitir ruídos de forma mais intensa, particularmente em baixas frequências. Em decorrência disso, a obtenção de uma boa relação entre peso e desempenho vibroacústico usualmente demanda algumas iterações de projeto. Nesse contexto, este trabalho tem por objetivo estabelecer um procedimento numérico para avaliar as propriedades vibroacústicas de placas flexíveis excitadas por um campo gerado no interior de uma cavidade acústica, bem como investigar a influência de parâmetros estruturais que definem a placa sobre o seu desempenho vibroacústico. O escopo aqui é a faixa de baixas frequências, na qual o comportamento do sistema é descrito de forma determinística através de características modais. Foi desenvolvido um modelo numérico em elementos finitos de uma cavidade acústica retangular de paredes rígidas acoplada a uma placa flexível. Uma fonte acústica posicionada no interior da cavidade produz um campo de pressão sonora que induz a placa à vibração e, consequentemente, a irradiar potência sonora para o campo livre exterior. Para realização das análises de sensibilidade, desenvolveu-se um conjunto de rotinas de modo a permitir o gerenciamento automatizado de simulações. Resultados numéricos são apresentados para avaliar a influência de diversos parâmetros estruturais sobre o desempenho vibroacústico da superfície estrutural. O procedimento proposto pode ser aplicado de forma eficiente para a análise de sensibilidade da transmissão de ruído em sistemas vibroacústicos sujeitos à variação de parâmetros estruturais e pode também ser utilizado para avaliar diversos tipos de materiais, como isotrópicos, ortotrópicos e até metamateriais. / Structural vibrations are the major causes of noise and people discomforts in several applications, such as in the products of the automotive, aerospace and naval industries, which are mainly composed of flexible plate-like structures. At the same time, the ever-increasing demands for energy efficiency and for reduced emissions of harmful gases into the environment lead product manufacturers of all industrial sectors towards an increased use of lighter materials. However, these solutions are most sensitive to issues related to vibroacoustic behavior, since the lightweight structures tend to present a high sound transmission, particularly at low frequencies. Consequently, the optimal design of lightweight and noise insulation properties of a structure usually require some design trade-offs. In this context, this dissertation aims to propose a numerical procedure to analyze the vibroacoustic performance of flexible plates subject to an interior acoustic field, as well as to investigate the influence of structural parameters on the sound insulation properties of the plate. The scope here is the low frequency range, in which the response of the coupled system is described in a deterministic way in terms of a mode set. A finite element model of a rigid rectangular acoustic cavity coupled to a flexible plate was developed. An acoustic source inside the cavity produces an interior sound pressure field that forces the flexible plate to vibrate and, consequently, to radiate sound power to the external free field. In order to enable the automatic management of the variability simulations, a set of routines was also developed. Numerical results are presented in order to evaluate the influence of several structural parameters on the vibroacoustic properties of the plate. The proposed methodology can be largely used in sensitivity analysis of noise transmission in vibroacoustic systems subject to the variation of structural parameters and can be used to evaluate many material types, as isotropic, orthotropic and even metamaterials.