Numerical Evaluation of the Forced Vibration Response of a Timoshenko Beam Subjected to a Moving Force Using the Modal Analysis Approach

The dynamic response of a structure subjected to moving loads is an interesting and meaningful research subject in various engineering fields such as bridges, roadways, railways and aircrafts. A vast number of studies has employed the vibration model of the Euler-Bernoulli beam to calculate the dynamic response of a beam structure under the action of moving loads. The present paper deals with the dynamic response of an uniform Timoshenko beam subjected to a moving force. Properties of the natural frequencies and modes of the Timoshenko beam are discussed. Using the modal method, a procedure for calculating the forced vibrations of the Timoshenko beam has been proposed. It is shown that the solution of the forced vibration for the transverse displacement and the rotation of the cross section of the beam can be expressed in form of a sum of two infinite series. The numerical simulation result shows that the speed change of the moving force has little effect on the beam deflection, but its magnitude change greatly affects the beam deflection.