Abstract
The problem of minimizing the dynamics response of a damped cantilever Timoshenko beam subjected to earthquake excitation is investigated in this paper. The ground acceleration is expressed in terms of a Fourier series that is modulated by an enveloping function. The method of lines and modal approach are developed for analyzing the eigenvalues and the flexural vibrations. A magneto rheological damper is proposed to reduce the vibration of the structure. The device is localized at a specific point of the beam. A modal shape which characterizes the vibration of the uncontrolled and controlled system is obtained. The condition of stability of the controlled system is derived using the Routh–Hurwitz criterion.
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