Dynamic analysis of a rectangular plate under a moving line load using scale beams and scaling laws

This paper presents a technique for predicting the dynamic responses of a two-dimensional (2-D) full-size rectangular plate undergoing a transverse moving line load (i.e., multiple concentrated loads located in a straight line) by using the one-dimensional (1-D) equivalent beam model or the scale beams subjected to a moving concentrated load, where the structural sizes and the external-load magnitude of the beam model are not necessarily equal to the corresponding ones of the plate model. In addition to the complete-similitude scale beams, the partial-similitude scale beams are also presented. It has been found that based on the scaling factors for partial similitude, some better scale beams may be established and one may have more choices for achieving the better model testing. The good agreement between the theoretical vibration responses of the 2-D full-size rectangular plate under a moving line load and the predicted ones obtained from the 1-D equivalent beam model or its scale beams under a moving concentrated load confirms the reliability of the presented theory. Because the scale model tests are cheaper and easier to be carried out, the presented technique will be meaningful from this viewpoint. The effort required by the presented technique based on the 1-D beam theory is also much smaller than that required by the conventional approaches based on the 2-D plate theory due to the fact that the order of overall property matrices for a beam model is much lower than that for the associated plate model.