Use of equivalent beam models for the dynamic analyses of beamplates under moving forces

For convenience, a rectangular plate with its two opposite shorter edges supported and the other two opposite longer edges free is called a beamplate in this paper. The dynamic analyses of either the beamplates or the general plates subjected to external moving loads are usually solved with the two-dimensional (2-D) plate model in the existing literature. The purpose of this paper is to present a one-dimensional (1-D) equivalent beam model to replace the last conventional 2-D plate model so that one may predict the dynamic behaviour of a 2-D beamplate due to a moving line load Pi=P (i=1–k), with that of a 1-D equivalent beam due to a moving single load, Fb, where the magnitude of the single load, Fb, is not necessarily equal to the summation of the line-load components, ∑i=1kPi. First of all, the requirements for the availability of the equivalent beam theory were presented. Next, the shape function method was used to calculate the equivalent nodal forces (and moments) so that the existing computer package may be used to tackle the present problem. Some factors having something to do with the feasibility of the presented theory, such as Poisson’s ratio, aspect ratio and eccentricity, were studied. Because the total number of finite elements (and nodal points) based on the 1-D equivalent beam model is much smaller than that based on the conventional 2-D plate model, one may achieve satisfactory results with much lower discretization and computational effort. Furthermore, although the presented theory is developed based on the single-span beamplate subjected to a moving line load, numerical examples reveal that it is also available for the cases of the multi-span beamplate (with multiple intermediate transverse line supports) subjected to a centric (or eccentric) moving single load.