الفهرس 
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Abstract
With the earthquake ground acceleration being the major source of continuous external disturbances, the vertical component effect on the bridge deck is lager than the horizontal component effect. Therefore artificial vertical component of earthquake with dominant frequency of 3.86 Hz is generating in this study. One of the purposes of this Thesis is to present a method of analysis for discrete beam upon implementing an active feedback control using the transfer matrix technique to reduce vibration of bridges deck under vertical earthquake component. The advantage of this method is that the response of the structure with an active feedback control can be obtained in a closed form and it provides a great insight and important information for the design of active control. Linear quadratic regulator (LQR) formulation is chosen to control system design due to its stability. The quadratic performance index is minimized based on the solution of the Hamilton equation. Steady state Riccati equation is used in closed loop with feedback of the slope and reaction force at support of the beam in first case, and feedback of displacement and ve10city of the midpoint of the beam in second case.
In the second approach the performance index is minimized at every time instant. Semi active control is considered as an active variab1e damper, where the damping coefficient of the device is varied to achieve the most reduction in the response. Standard control theory is difficult to apply in a straightforward fashion in this case because the equation of motion includes the damping coefficient, which needs to be controlled instantaneously. The equation of motion is nonlinear in the sense that the control uses feedback information involving the structural response itself.
Two algorithms for selecting the damping coefficient of variable dampers are proposed and compared for reducing oscillations of flexible and rigid beams. The first algorithm, is a refinement of the bang-bang algorithm. In the second algorithm an instantaneous optimal control is used to control the damping coefficients. The results of these algorithms are compared with passive damper to assess the effectiveness of the variable
damper.
Hybrid control is also studied considering an active tuned mass damper (ATMD). A
closed -loop velocity and displacement feedback control algorithm is proposed for control system. Minimizing the displacement and velocity of the midpoint of the beam where the damper is mounted derives the gains coefficients of the actuator. The control
effects of the A TMD with optimal and non-optimal passive control device are discussed. Comparisons are also made on the control efficiency between A TMD, TMD and active control system alone. The effects of these control algorithms on the reduction of absolute acceleration and relative displacement are examined for deck bridges. It is shown from theoretical and numerical results that the proposed A TMD control system is very effective in reducing the response of bridge under earthquake load. The results also show that for the same level of reduction in beam displacements, the control force required using ATMD is smaller than active control alone. Therefore promising results are obtained in reducing seismic responses.