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In this paper we study the behavior of a semi-active suspension witch external vibrations. The mathematical model is proposed coupled to a magneto rheological (MR) damper. The goal of this work is stabilize of the external vibration that affect the comfort and durability an vehicle, to control these vibrations we propose the combination of two control strategies, the optimal linear control and the magneto rheological (MR) damper. The optimal linear control is a linear feedback control problem for nonlinear systems, under the optimal control theory viewpoint We also developed the optimal linear control design with the scope in to reducing the external vibrating of the nonlinear systems in a stable point. Here, we discuss the conditions that allow us to the linear optimal control for this kind of non-linear system.

The vortex-induced vibrations may have disastrous effects in engineering practice, affecting significantly the durability, reliability and safety of engineering structures. This is a reason for which a great deal of effort has been dedicated to the proposition of control strategies to deal with the vortex-induced vibration problem. However, few works have proposed the use of viscoelastic materials to suppress the vibrations induced by vortex shedding, which motivates the present study. Here, the immersed boundary method combined with the virtual physical model is used to investigate the dynamics of a viscoelastically-mounted rigid cylinder in a fluid flow under transverse oscillations induced by vortex shedding. A straightforward time-domain modeling procedure of immersed viscoelastic system by using a four-parameter fractional derivative model is proposed. After the theoretical aspects, numerical tests are performed to investigate the vortex-induced oscillations and flow characteristics of the immersed viscoelastic system at Reynolds number 10,000 for a range of reduced velocity and temperature for two values of mass ratios. The results demonstrate the interest in using viscoelastic materials to mitigate the vortex-induced vibrations.

Aos meus pais Claiton e Lúcia pela dedicação, suporte, incentivo, carinho, amor e por fornecer o maior tesouro e herança que uma pessoa pode ter que é o conhecimento. À minha irmã Isabela pelo companheirismo e amizade que temos. À minha namorada Naianne pelo suporte, companheirismo, compreensão, conselhos, carinho, amizade durante a realização deste e outros projetos. À todos os companheiros do laboratório LMEst. Ao meu orientador Professor Dr. Antônio Marcos Gonçalves de Lima pelos ensinamentos e dedicação ao longo desse projeto. Para minha co-orientadora Dra. Alice Rosa da Silva pela ajuda em compartilhar o conhecimento e colaboração prestada nesse trabalho. Ao CNPQ pelo apoio financeiro durante o desenvolvimento dessa dissertação.

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