Wave radiation in a one-dimensional system due to a non-uniformly moving constant load

The wave radiation in an elastically supported infinite string due to a sudden change in the velocity of a constant moving vertical load is studied. It is shown that radiation results from the transition of the eigenfield moving with the load. In this process both the vertical load and the horizontal, force maintaining the motion after the velocity change, are performing work. The energy variation law has been verified, showing that the change of the energy in the eigenfields of the load and the radiated energy is equal to the work done by the moving vertical load and the horizontal force maintaining the motion after the velocity change. To visualize the process of radiation after the velocity jump the transient vibrations of the string have been determined. It shows that the eigenfield of the load before the velocity change is transferred to a new eigenfield by going through a so-called formation zone in which waves are radiating out in both directions.