Application of the Optimal Preview Control Theory to the Vibration Reduction of the Elastic Beam under Moving Load

Abstract

In this paper, the vibration reduction problem of simply supported beam excited by distributed random moving load is investigated. The optimal transfer functions of preview filters, of which input is the future value of random load picked up at upstream position are obtained by solving the matrix Wiener-Hopf integral equations. The properties and control effects are shown numerically for two concrete examples. The results are compared with that of the system with passive elements in order to certify the effects of control. That is, the mean square deflection of beam corresponding to a certain constraint on the force transmitted by the controller is reduced in comparison with that of the system with passive elements, and it is further reduced with increasing of preview time to some extent.