Uso da base dinâmica em um sistema de duas vigas acopladas

• Ano de defesa: 2013
• Autor(a) principal: Seibel, Aline Brum
• Orientador(a): Copetti, Rosemaira Dalcin
• Banca de defesa: Carvalho, João Batista da Paz , Chiwiacowsky, Leonardo Dagnino
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática
• Departamento: Matemática
• País: BR
• Palavras-chave em Português: Viga Euler-Bernoulli dupla; Base dinâmica; Frequências e modos de vibração; Resposta impulso matricial; Amortecimento de rayleigh
• Palavras-chave em Inglês: Euler-Bernoulli double beam; Dynamic basis; Frequencies and vibrations modes; Impulse response matrix; Rayleigh damping
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/9986

This work researches on free and forced vibrations of a double beam coupled system. The system is regarded as two Euler-Bernoulli beams which are parallel, have the same length, are simply supported and are connected through a viscoelastic layer. Natural frequencies and their mode shapes, also called eigenfunctions, of the coupled system are obtained through a uniform beam methodology which uses the free dynamical basis to represent the solution of the the modal equation. This study uses modal analysis and block matrix formulation, while the dynamical basis used to represent the modal solution is obtained from the dynamical solution of a fourth order differential equation whose coefficients are just those of the original problem. The natural frequencies and mode shapes of the undamped system are determined for several values of beam parameters. For the damped case, damping ratios of each beam and also of the viscoelastic layer (which characterizes the coupling the system) are considered. The forced response is represented using matrix impulse response, which is the solution of an initial value problem with impulsive initial conditions.