Traveling Waves in Beam on Elastic Foundation

Abstract

The dynamic response of an infinitely long beam on elastic foundation was analyzed by the method of direct analysis. The conditions analyzed included a step sustained loading with two values of spring constant in the foundation, and rectangular pulse loadings with seven pulse durations. The results of the analysis for the sustained loading agreed very well with an available solution. Also, for rectangular pulse loadings the relationship between the dynamic response factor and the ratio of pulse duration to the natural period of the beam‐foundation system was found to be slightly different from that of the single‐degree‐of‐freedom system. The behavior of the beam for the very short time immediately after application of the load is analyzed via some typical cases. The method of direct analysis is a numerical approach which by‐passes the derivation and use of differential equations. Instead, the actual statements of the governing physical laws are applied directly to the beam‐foundation system. The physical laws used are equations of motion and constitutive relations. In spite of some limitations, the method can be used with arbitrary loadings in position and time. It is concluded that the method of direct analysis is a very effective tool for dynamic analysis of beam on elastic foundations.