Complex Infinite Beams on Elastic Foundation

Simple infinite beams on an elastic foundation have presented few problems, in fact they are usually easier to solve than beams of finite length. For some time it has been possible to analyze with relative ease finite beams with arbitrary loading and foundations. The transfer matrix method is particularly useful in the static, stability, and dynamic study of beams with many changes in cross-sectional and support properties. Most available techniques encounter difficulties when applied to very long beams. It is the purpose of this paper to show how the transfer matrix method for beams of finite length can be extended to encompass beams of infinite length. With this approach it is possible to analyze, without encountering numerical instability, infinite or semi-infinite beams with any loading or arbitrary changes in properties along the beam.