Laplacian differential operator -- Vibrations of plucked strings and Hollow cylinders.

In 1966 Mark Kac posed an interesting question regarding vibrating membranes and the sounds they make. His article entitled "Can One Hear the Shape of a Drum?", which appeared in The American Mathematical Monthly, generated much interest and scholarly debate. The evolution of Kac's intriguing question will be the subject of this project.

Much progress has been made in recent years in active control of sound radiation from vibrating structures. Reduction of the far-field acoustic radiation can be obtained by directly modifying the response of the structure by applying structural inputs rather than by adding acoustic sources. Discontinuities, which are present in many structures are often important in terms of sound radiation due to wave scattering behavior at their location. In this thesis, an edge or boundary type discontinuity (clamped edge) and a point discontinuity (blocking mass) are analytically studied in terms of sound radiation. When subsonic vibrational waves impinge on these discontinuities, large scattered sound levels are radiated. Active control is then achieved by applying either control forces, which approximate shakers, or pairs of control moments, which approximate piezoelectric actuators, near the discontinuity. Active control of sound radiation from a simply-supported beam is also examined. For a single frequency, the flexural response of the beam subject to an incident wave or an input force (disturbance) and to control forces or control moments is expressed in terms of waves of both propagating and near-field types. The far-field radiated pressure is then evaluated in terms of the structural response, using Rayleigh's formula or a stationary phase approach, depending upon the application. The control force and control moment magnitudes are determined by optimizing a quadratic cost function, which is directly related to the control performance. On determining the optimal control complex amplitudes, these can be resubstituted in the constitutive equations for the system under study and the minimized radiated fields can be evaluated. High attenuation in radiated sound power and radiated acoustic pressure is found to be possible when one or two active control actuators are located near the discontinuity, as is shown to be mostly associated with local changes in beam response near the discontinuity.. The effect of the control actuators on the farfield radiated pressure, the wavenumber spectrum, the flexural displacement and the near-field time averaged intensity and pressure distributions are studied in order to further understand the control mechanisms. The influence of the near-field structural waves is investigated as well. Some experimental results are presented for comparison. / Ph. D.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Sciences. / Microfiche copy available in Archives and Science. / Bibliography: leaves 122-123. / by Charles A. Moo. / Ph.D.

The theory of the scattering of plane waves in a fluid medium by an isotropic elastic sphere representing a manganese nodule is developed. Scattering cross sections were computed using the theory and the results are presented graphically. The scattering cross section and the reflectivity factor govern the characteristic acoustic signature of the Pacific where manganese nodules are present. Preliminary experimental data for the compressional and shear wave speeds in nodule material is given. This data was used in the scattering computations. Limiting cases of Rayleigh scattering and scattering from fixed rigid and fluid spheres are also shown for comparison. It is shown that the rigidity of the nodules dominates the high frequency response. The problem of the multiple scattering of acoustic waves by randomly distributed nodules on the flat ocean bottom is investigated analytically. The statistical description of nodule deposits is given. The concept of the configurational average is introduced in order to obtain the average scattered response. The size averaging is found to be able to smooth the acoustic response in the high frequency region. The plane wave analysis for the multiple scattering problem is justified by the narrow beam investigation. It shows that the beam effect on the average backscattered field can be neglected in the remote sensing. For a planar distribution of nodules, the average scattered field excited by a normally incident plane wave is verified to be plane waves characterized by coherent reflection and transmission coefficients. The multiple scattering effect is found to be a higher order correction to the average scattered field. For a sparse distribution of nodules, the average scattered field can be well evaluated using the single scattering theory in which the scattering process is also shown to be energy conserved. For a dense distribution of nodules, the radial distribution function is used in the Foldy-Lax hierarchy. The result shows that the pair correlation affects the phase of the second order correction term in the expression for the average scattered field when the higher order statistics are truncated using the quasi crystalline approximation. / Ph. D.

An investigation is presented of the behavior of time-reversal focusing in soils. Initial numerical models demonstrate time-reversal focusing to be effective in elastic media, including when a large number of scattering objects were present in the medium. When scattering objects are present, time-reversal focusing demonstrates superior focusing ability when compared to other excitation methods such as uniform excitation or time-delay focusing. Multiple experimental investigations of experimental time-reversal focusing performed in sand evaluate time-reversal focusing effectiveness when multiple near-surface scattering objects are present in the medium. Experimental results demonstrate that time-reversal focusing is effective in the experimental context as well as the numerical models. Further experiments examine time-reversal focusing in more extreme cases where the entire ballistic wave is blocked, and the only energy reaching the focus point is reflected from scattering objects in the medium. A comparison to other focusing methods demonstrates that under these conditions, most focusing attempts with traditional methods will fail completely while time-reversal focusing does not. Additional configurations of time-reversal focusing examine its effectiveness when scattering is caused by an asymmetrical surface layers. The impact of an asymmetrical or non-uniform excitation array is also examined for time-reversal focusing in the presence of scattering objects. An investigation of the effects of scattering object geometry on focusing resolution in time-reversal focusing is also presented. Scattering object field density is found to have a strong, but diminishing effect on focusing resolution as the scattering object field density increased. Loss of surface wave energy available for focusing due to mode-conversion is found to be correlated with the density of the scattering object field. The impact of the weak non-linear nature of the soil on time-reversal focusing is examined through a study of time-reversal focusing behavior for a variety of amplitudes that generate different levels of non-linearity in the soil. This study of nonlinearity is coupled with a study of the impact of noise on time-reversal focusing. It appears that both non-linearity and noise have an impact on time-reversal focusing effectiveness. Further, the loss from these mechanisms seems to be interrelated. Noise seems to enhance non-linear loss in the soil.

In shallow water environments, sound propagation experiences multiple interactions with the surface/bottom interfaces, with hydrodynamic disturbances such as internal waves, and with tides and fronts. It is thus very difficult to make satisfactory predictions of sound propagation in shallow water. Given that many of the ocean characteristics can be modeled as stochastic processes, the statistical measure, spatial coherence, is consequently an important quantity. Spatial coherence provides valuable information for array performance predictions. However, for the case of long-range, low frequency propagation, studies of spatial coherence influenced by various environmental parameters are limited insofar as having the appropriate environmental data with which to model and interpret the results. The comprehensive Asian Seas International Experiment 2001 (ASIAEX01) examined acoustic propagation and scattering in shallow water. Environmental oceanographic data were taken simultaneously with the acoustic data. ASIAEX01 provided a unique data set which enabled separate study of the characteristics of the oceanographic features and their influence on long range sound propagation. In this thesis, the environmental descriptors considered include sediment sound speed and attenuation, background internal waves, episodic non-linear internal waves, and air-sea interface conditions. Using this environmental data, the acoustic data are analyzed to show the characteristics of spatial coherence in a shallow water waveguide. It is shown that spatial coherence can be used as an inversion parameter to extract geoacoustic information for the seabed. Environmental phenomena including internal waves and wind-generated surface waves are also studied. The spatial and temporal variations in the sound field induced by them are presented. In addition, a tank experiment is presented which simulates propagation in a shallow water waveguide over a short range. Based on the data model comparison results, the model proposed here is effective in addressing the major environmental effects on sound propagation in shallow water.

Submitted by Jordan (jordanbiblio@gmail.com) on 2017-04-25T13:41:33Z No. of bitstreams: 1 DISS_2015_Muriel André de Moura.pdf: 2679936 bytes, checksum: 0f316281e790173daa1fca114f65c028 (MD5) / Approved for entry into archive by Jordan (jordanbiblio@gmail.com) on 2017-04-27T14:11:34Z (GMT) No. of bitstreams: 1 DISS_2015_Muriel André de Moura.pdf: 2679936 bytes, checksum: 0f316281e790173daa1fca114f65c028 (MD5) / Made available in DSpace on 2017-04-27T14:11:34Z (GMT). No. of bitstreams: 1 DISS_2015_Muriel André de Moura.pdf: 2679936 bytes, checksum: 0f316281e790173daa1fca114f65c028 (MD5) Previous issue date: 2015-03-10 / A presente pesquisa objetiva desenvolver e aplicar, para alunos do ensino médio, um produto educacional para o ensino de ondas sonoras na disciplina de Física. Esse produto educacional, composto de três aulas teóricas e uma prática, culmina com a montagem de um aparato experimental. Esse aparato é montado facilmente a partir de materiais de baixo custo. O mesmo funciona captando as ondas sonoras e as transformando em figuras semelhantes às Figuras de Lissajous. Para a avaliação desse produto educacional foi utilizada a Teoria da Aprendizagem Significativa de David Ausubel e a pesquisa qualitativa. Dessa forma, foi possível investigar e obter evidências de aprendizagem significativa por parte dos alunos participantes das aulas. / The present research aims at the development and application, with students from high school, of an educational product for the teaching of sound waves under the discipline of Physics. This educational product, composed of three theoretical classes and one practical one, culminates with the assemblage of an experimental apparatus. That apparatus is easily mounted from low cost materials. It works by detecting the sound waves and converting them in figures alike the Lissajous Figures. In order to evaluate this educational product the Theory of Meaningful Learning from David Ausubel was used, as well as the qualitative research. That way, it was possible to investigate and to collect evidences of meaningful learning by the participating students.

Made available in DSpace on 2014-10-09T12:38:39Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:05:15Z (GMT). No. of bitstreams: 1 06042.pdf: 9369626 bytes, checksum: 37950a2f878d6535f671de4a025da71c (MD5) / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Orientadores: José Roberto de França Arruda, Philippe Herzog / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-16T06:12:24Z (GMT). No. of bitstreams: 1 Pasqual_AlexanderMattioli_D.pdf: 10340586 bytes, checksum: 74b86a8897be1f1c00e3c13b018e73bb (MD5) Previous issue date: 2010 / Resumo: O controle angular da radiação sonora pode ser obtido utilizando um arranjo compacto de alto-falantes independentemente programáveis operando na mesma faixa de frequência. Geralmente, os alto-falantes são dispostos sobre uma estrutura de formato esférico seguindo a geometria de um sólido de Platão a fim de se obter uma configuração altamente simétrica. Recentemente, protótipos de arranjos esféricos compactos de alto-falantes vêm sendo desenvolvidos e aplicados a medições em acústica de salas, performances de música eletroacústica e síntese de padrões de diretividade de fontes acústicas tais como instrumentos musicais. Contudo, muitos aspectos referentes a seu controle, projeto e comportamento eletromecânico, bem como à sua habilidade em proporcionar uma experiência sonora mais realista que sistemas de áudio convencionais, permanecem não esclarecidos. Este trabalho contempla a análise e síntese de campos sonoros através de um arranjo esférico compacto de alto-falantes e pretende contribuir para o esclarecimento de alguns aspectos supracitados. Propõe-se uma estratégia de controle baseada nos modos de radiação acústica do arranjo esférico, a qual apresenta várias vantagens sobre a estratégia usual fundada nos harmônicos esféricos. Uma análise teórica e experimental do comportamento eletromecânico de arranjos compactos de alto-falantes também é apresentada, na qual o acoplamento acústico entre os alto-falantes no interior da estrutura esférica é considerado. Além disso, os sinais ótimos dos alto-falantes correspondentes a um dado padrão de diretividade são calculados utilizando duas funções custo distintas, revelando que o realismo do padrão sintetizado pode ser significativamente ampliado desprezando-se a fase da diretividade alvo. Finalmente, os modelos teóricos propostos são validados por medições de impedância elétrica, velocidade dos diafragmas dos alto-falantes e padrões de diretividade / Abstract: Angular control of the sound radiation can be achieved by using a compact array of independently programmable loudspeakers operating at the same frequency range. The drivers are usually distributed over a sphere-like frame according to a Platonic solid geometry to obtain a highly symmetrical configuration. Prototypes of compact spherical loudspeaker arrays have been recently developed and applied in room acoustics measurements, electroacoustic music performance and synthesis of directivity patterns of acoustical sources such as musical instruments. However, many aspects concerning their control, design, electromechanical behavior and ability to provide a more realistic sound experience than conventional audio systems remain unclear. This work concerns the analysis and synthesis of sound fields by a compact spherical loudspeaker array and aims to contribute to clarifying some aspects mentioned above. A control strategy based on the acoustic radiation modes of the spherical array is proposed, which presents several advantages over the usual strategy based on the spherical harmonics. A theoretical and experimental analysis of the electromechanical behavior of compact loudspeaker arrays is also presented, in which the acoustic coupling between drivers inside the array frame is taken into account. In addition, optimumdriver signals corresponding to a given target directivity pattern are derived using two different cost functions, indicating that the realism of the synthesized pattern may be significantly increased by neglecting the phase of the target directivity pattern. Finally, the proposed theoretical models are validated through measurements of electrical impedance, loudspeaker diaphragm velocity and directivity patterns / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica