Estabilidade assintótica e numérica de sistemas dissipativos de vigas de Timoshenko e vigas de Bresse

• Autor(a) principal: Almeida Junior, Dilberto da Silva
• Data de Publicação: 2009
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/168
• topic: Equações diferenciais parciais; Sistemas de Timoshenko; Sistemas de Bresse; Método de diferenças finitas; Semi-discretizacões; Differential equations, Partial; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::EQUACOES DIFERENCIAIS PARCIAIS

In this thesis we study models of plane beams governed by Timoshenko s hypothesis and models of curved beams governed by Bresse s hypothesis in the presence of dissipative mechanism, which act partially on the rotation function in the transverse section or on the transverse displacement ones. We realize an analytic study of these models and we show they are exponentially stable, if and only if, the velocities of wave propagations are equal. Such result is more interesting on the point of mathematical view whereas in the practice the velocities of wave propagations are never equal. We study in the general case the polynomial stability property and we show the dissipative systems are stable and, in these situations, the decay rate can be improved according to the regularity of the initial data. In the specific cases of the models of curved beams, the differential factor is in the mathematical techniques we use, which they are much more sophisticated. Finally we realize a numerical study of the dissipative models using semi-discrete and totally discrete models in finite differences, purposing to avoid the problem of shear locking and to we confirm the theoretical results developed here.