Made available in DSpace on 2015-05-14T12:14:07Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1512497 bytes, checksum: 049664bc02f2d2d336fd5fe2822b8458 (MD5) Previous issue date: 2013-03-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Granular decorated chains can be used for the development of impact-absorbing devices. Thus, one of the features of those systems is that they can be used as shock absorbers and impact protectors. We study here the pulse propagation in a decorated granular chain, composed of spherical grains, which initially are just touching each other, making use of an effective description, where the original chain was replaced by a decorated chain with effective masses where the grains interact via an effective potential. Our goal was to generalize the results obtained in a previous work, by analizing a decorated chain with an arbitrary number of small grains between the large ones, and thus, presenting an analytical approach that describes the effective masses and the effective interaction between the granules as a function of the quantity small grains between the large ones. In this system the grains interact with each other via the Hertz potential. We presented the comparation between of the numerical and analytical results for the profiles velocity of the large granules in the original chain with the grains of the effective chain, the pulse propagation time, and the frequency of oscillation of the smaller grains in the original chain. We also highlight the use of Binary Theory, which was been widely appllied to describe analitically the properties of the propagating pulse in granular chains. / Cadeias granulares decoradas podem ser usadas no desenvolvimento de aparelhos que visam absorver ondas de choque. Sendo assim, uma das características deste sistema ´e que eles podem ser usados como absorvedores de choque e na proteção contra impactos. Estudamos aqui a propagação de um pulso em uma cadeia granular decorada, composta de grãos esféricos, que inicialmente estão apenas se tocando, fazendo uso de uma descrição efetiva, onde a cadeia original decorada ´e substituída por uma cadeia não decorada com massas efetivas onde os grãos interagiam através de um potencial efetivo. Nosso objetivo foi generalizar os resultados obtidos em um trabalho anterior, analisando uma cadeia decorada com um número qualquer de grãos pequenos entre os maiores, e assim, apresentando uma abordagem analítica que descreve a massa efetiva e a interação efetiva entre os grãos em função da quantidade de grãos pequenos entre os maiores. Neste sistema os grãos interagem através do potencial de Hertz. Apresentamos a comparação entre os resultados numéricos e analíticos, para os perfis de velocidade dos grãos grandes da cadeia original com os grãos da cadeia efetiva, além da comparação do tempo de propagação do pulso, e a frequência de oscilação dos grãos menores na cadeia original. Destacamos também o uso da Teoria Binária, que tem sido bastante aplicada para descrever analiticamente as propriedades da propagação de um pulso em cadeias granulares.

The theory of the lamellar eutectoid reaction by volume diffusion has been extended to account for solute segregation within the product phases and the effect of dilute third element additions. It has been demonstrated for symmetric binary systems that the segregation can account for 10% or more of the free energy stored in the product phases and can lead correspondingly to a predicted lamellar spacings appreciably greater than those obtained when segregation is neglected. This segregation is relatively high in the systems Cu-In, Cu-Be and Ag-Cd and may account for the fact that a secondary coarse-grained pearlitic reaction follows the initial fine grained one in these systems. The binary theory has been-used to analyse the available data for the eutectoid reaction in the Cu-Al and Fe-C systems and satisfactory agreement is obtained. The theory for ternary systems, while complete in principle, proves to be. intractable in all but the simplest version of the solution thermodynamics. It is concluded that the effect of the third element on the binary eutectoid reaction is mainly through its effect on the phase diagram, the ternary cross effects in the diffusion matrix tending to cancel out. Any additional element which lowers the eutectoid temperature will retard the reaction. / Thesis / Doctor of Philosophy (PhD)

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