Vibrations of sandwich beam due to a moving force

We study dynamic response of a finite, simply supported sandwich beam subject to a force moving with a constant velocity. The classical solution has a form of an infinite series. The main goal of this paper is to show that the aperiodic part of the solution can be presented in a closed form instead of an infinite series. The presented method of finding the solution in a closed form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. The closed solutions take different forms depending if the velocity v of the moving force is smaller or bigger than the shear-wave velocity of the beam. The solution for the dynamic response of the sandwich beam under moving force is important because it can be used also in order to find the solution for other types of moving loads.