Analysis of the free vibration of a beam on a deformable support using a generalised analytical continuum model

This paper deals with the application of a generalised analytical continuum foundation model recently proposed by the senior author to the dynamic analysis of beams. Specifically, analytical and numerical solutions of the problem of the free vibration of a beam on an equivalent two-parameter model and a simplified Winkler-type model are presented. In the two-parameter representation, a novel approach is used in which the shear parameter is taken care of by moving it from the soil-beam interface to the beam proper in the form of a geometric stiffness so that it serves as an enhancement to the conventional elastic beam stiffness. By doing so, the familiar Winkler support is maintained while the shear interaction among the springs is realised at the same time. Additional end springs are introduced to account for the shear continuity extending beyond the ends. The analytical and numerical results are compared with those obtained from the finite element software, Abaqus, by means of which the calibration factor is determined. The model is validated using measured data from the literature. The results are also compared with other existing models. Both the single- and two-parameter variants of the model performed remarkably well, especially the two-parameter variant.