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Master's Dissertation
DOI
Document
Author
Full name
José Renato Alcarás
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Ribeirão Preto, 2019
Supervisor
Committee
Martinez, Alexandre Souto (President)
Baggio, André Luis
Carneiro, Antonio Adilton Oliveira
Silva, Glauber José Ferreira Tomaz da
Title in Portuguese
Espalhamento de ondas acústicas e análise de campos internos de materiais viscoelásticos
Keywords in Portuguese
Acústica
Espalhamento
Materiais viscoelásticos
Abstract in Portuguese
O espalhamento de ondas de som tem por objetivo compreender a natureza de propagacao de ondas sonoras incidentes e espalhadas, para diferentes estruturas e geometrias dos centros espalha- dores que formam um meio desordenado. Na literatura, em geral, obtemos informacoes relativas ao espalhamento acustico em regioes distantes dos centros espalhadores (aproximacao de campo distante), para algumas formas de onda incidentes e de particulas espalhadoras. Buscando compre- ender o comportamento ondulatorio em regioes proximas ao centro espalhador e em seu interior, nosso estudo fornece uma descricao analitica dos campos de radiacao acustica nessas regioes. Ini- cialmente, considera-se o problema do espalhamento de uma onda plana acustica plana (viajando num fluido ideal newtoniano) por uma particula esferica fluida, com caracteristicas distintas das do fluido inicial. Ainda, calculamos a energia interna armazenada nesse centro espalhador como funcao do volume da esfera espalhadora, bem como do comprimento da onda em seu interior, de sua amplitude e da densidade do centro espalhador. Posteriormente, os materiais espalhadores sao considerados de natureza viscoelastica (que apresentam comportamentos viscosos e elasticos sob a acao de forcas externas), por serem viaveis na modelagem de celulas biologicas e polimeros, em geral. Para isso, tratamos formalmente da fisica de materiais elasticos, como deformacoes e tensoes, a fim de respaldar o tratamento do modelo viscoelastico de Kelvin-Voigt fracionario usado em nosso estudo. Obtivemos formulas fechadas para os coeficientes de espalhamento (bem como os coeficientes das ondas internas ao centro espalhador) desse problema em questao, a partir da solucao de um sistema linear de equacoes. Os resultados permitem a construcao de uma teoria de base para um estudo generalizado do espalhamento de ondas acusticas por materiais viscoelasticos, perspectiva a ser conduzida num futuro proximo.
Title in English
Acoustic wave scattering and internal fields analysis of viscoelastic materials
Keywords in English
Acoustics
Scattering
Viscoelastic materials
Abstract in English
The sound wave scattering aims to understand the propagation nature of scattered and incident sound waves, for different structures and geometries of the scattering centers that form a disordered environment. In the literature, in general, we obtain information regarding the acoustic scattering in regions distant from the scattering centers (far-field approximation), for some incident wave- forms and scattering particles. In order to understand the undulatory behavior in regions close to and within the scattering center, our study provides an analytical description of the acoustic radiation fields in these regions. First, the problem considered is the scattering of an acoustic plane wave (previously traveling through an ideal newtonian fluid) by a spherical fluid particle, with distinct acoustic characteristics from the initial fluid. Still, it is determined the internal acoustic energy stored in this scattering center, as a function of the scattering spheres volume, as well as the wavelength in its interior, its amplitude and the density of the scattering center. Later, the scattering materials are considered to be viscoelastic (which exhibit viscous and elas- tic behavior when subjected to external forces), as they are feasible in the modeling of biological cells and polymers in general. For such, we deal formally with elastic materials physics, such as deformations and tensions, in order to deal with the Kelvin-Voigt viscoelastic model used in this problem. Were determined closed formulas for the scattering coefficients for this problem (as well as the internal wave coefficients), from the solution of a linear system of equations. The results allow the construction of a fundamental theory for a generalized study of sound wave scattering by viscoelastic materials, which is a goal to be achieved in a near future.
 
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Publishing Date
2019-06-26
 
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