Dynamic Response of Beams on Elastic Foundation

Abstract

A method is proposed for dynamic analysis of beams on an elastic foundation. The method develops mass and stiffness matrices of a beam on an elastic foundation finite element from the exact solution of the shape functions governing its end deformations. The developed matrices can be combined with conventional beam element matrices to obtain assembled matrices, which can be used to determine natural frequencies and mode shapes of a general structure. Since the proposed method is based on the exact solution of the related differential equation, the accuracy is independent of element refinement. This is in contrast to other methods in which the accuracy is dependent on the number of elements modeled due to approximate modeling of the elastic foundation as discrete soil springs. The proposed method can be further expanded for forced vibration problems, such as earthquake problems, to determine dynamic response under time varying loads. Numerical examples are presented to demonstrate the effectiveness of the proposed method.