The work presents a finite element modeling of beam resting on a two-parameter layered soil. The behavior of the soil continuum and the beam are assumed to be linear and homogeneous isotropic. Using the strain energy expressions, the shear strain of the beam element and the soil foundation are taken together in the analysis. In this approach, the stiffness matrix of each component is elaborated and integrated in the finite element analysis. First, various examples are elaborated to show the effectiveness of the proposed approach and the ability of the numerical program developed for this concern. Second, the analysis is widened to study the influence of the soil properties on the interface continuum and on the beam responses. Third, a parametric study is carried out to highlight the effect of the position of springs at the interface continuum, the properties of soil, the deepest of the soil foundation and the ballast layer on the response of the interface and the beam itself. Moreover, shear deformations are presented to show the crucial influence on the beam, on the structure and on the interface behaviors. Obtained results show pertinent results corresponding to the interface continuum and the beam responses.

This paper describes the dynamic analysis of soil-structure interaction by using the spectral element method (SEM). This numerical method is a powerful numerical technique suited for the dynamic tasks. In this case, numerical methods with highly developed computer technique become very efficient to analyze complex problems. The partial differential equation governing the motion is derived and solved by using SEM. Thus, the corresponding solutions are the eigenvalues of the problem, so natural frequencies are tabulated for the first three modes of vibration. This numerical analysis treats the effect of: (a) the modal analysis with and without the elastic medium, (b) the influence of the interaction between the beam and soil, (c) the influence of the soil properties on the dynamic response, and (d) the influence of the non-classical boundary conditions. The obtained results of these effects are presented and commented.

This paper describes the effects of soil non-homogeneity, the soil–structure interaction and the two-parameter elastic foundation model on the free vibration of Euler–Bernoulli beams. Non-homogeneity of the soil foundation is described by parabolic variations of the two-parameter elastic soil foundation while Poisson's ratio is assumed to remain constant. Hence, the soil–structure interaction is quantified using a relative ratio of beam and soil foundation properties. The equation of motion including the previous effects is derived and the fundamental frequency parameters are computed. The influence of the above parameters on the free-vibration characteristics of the beam is investigated. The results obtained from this analytical method for a simply supported beam were found to be in very good agreement with data from the literature.