Vibrations of axially compressed sandwich beam due to a moving force

Abstract

The dynamic response of a finite, simply supported axially compressed sandwich beam subject to a force moving with a constant velocity is investigated. The classical solution has a form of an infinite series. The main goal of this paper is to present that the aperiodic part of the solution can be presented in a closed form instead of an infinite series. The shown method of finding the solution when the form is closed 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 on the velocity v of the moving force is smaller or bigger than the shear-wave velocity of the beam. The dynamic response of the sandwich beam under moving force is very important solution. It is because that it can be used also in order to find the solution for other types of moving loads.