Statics and dynamics analysis of interactions between Euler Bernoulli beams including poisson ratio effect and winkler foundations

In this study, Euler Bernoulli beam model including the Poisson ratio effect is obtained. Soil-structure interaction (SSI) analyses are necessary in design of foundation piles and beams lying on foundations. It is well-known that SSI has considerably role on the behavior of the beam or pile. Therefore, the proposed beam is thought to interact with the soil. The soil is modeled with widely used Winkler foundation model. In this model, the soil is considered as an elastic, infinite number of independent spring. Three different soil types is considered. The equations of motion and boundary conditions of the beam lying on Winkler foundation is derived via adopting the extended Hamilton principle. The equation is non-dimensionalized to obtain universal results. The dimensionless equation is solved by Galerkin method and the natural frequency values of the beam in different foundation spring coefficients are obtained for hinged-hinged support condition. This new equation is used to investigate the soil-structure interaction features of the beam with varying sectional area. It is seen that the natural frequencies of the beam is decreasing with the Poisson's ratio. Finally, the effect of the Poisson's ratio and foundation spring coefficient on the behavior of the proposed beam is discussed and demonstrated through given diagrams.