Active damping of vibrations of one dimensional continuum under a moving load

In this paper, a semi-active control of vibrations of ID elastic continuum under a traveling load is presented. Bridge spans induced by vehicles traveling over it with high speed can be reinforced by supplementary supports with magneto or electroreological dampers controlled externally. Structures with such an external control of parameters can resist to the load in a more efficient way. Controlled system widely outperforms passive cases when decreasing amplitudes of transverse vibrations. The goal of the paper is to design a control method - effective and simple in practical realization. In the model the number of dampers and their fixed points are taken as arbitrary. Control functions are assumed to be piecewise constant. Response of the system is solved in modal space. Full analytical solution is based on the power series method and is given in an arbitrary time interval. The performance of assumed strategy is verified for different cost integrands. Several examples are solved by using the proposed method.