Reduction of vibration on a cantilever Timoshenko beam subjected to repeated sequence of excitation with magnetorheological outriggers

This paper deals with the statistical effects of an outrigger system on a cantilever beam under seismic excitation. The nonstationary random approach is employed to simulate seismic events. The Timoshenko beam approach is used to model the frame‐core tube linked at a point of its length by the damped outriggers, therefore are connected vertically two magnetorheological damper devices. The peak root‐mean‐square values of displacement responses is employed as a best measure effective to specify the optimal locations of outriggers according to different vibration modes. To evaluate the performance of the control system, the control algorithm based on Lyapunov stability theory is adopted to seek the input voltage leading to the reduction of vibration.