Effect of soil coefficients and Poisson’s ratio on the behavior of modified Euler-Bernoulli beam lying on Winkler foundation

Abstract

Beside the geometric acceptations on deriving the mathematical model of the structural elements the material specifications can affect their different fundamental responses. Respectively, in this study standard Euler-Bernoulli beam theory is adjusted and modified to comprise the effect of Poisson’s ratio on the mechanical model of the beam. The interaction between beams and the soil medium below the beams alter the actual behavior of the beams. In this study, the equation of motion of the beam lying on Winkler foundation is derived via adopting the extended Hamilton principle. This new formulation is used to investigate the soil-structure interaction features of the modified beam with uniform cross sectional area. Three different soil types is considered. The non-dimensional mathematical model of the proposed beam is also obtained. 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.

Keywords

• Euler-Bernoulli beam

Kaynakça

1. [1] Dutta S.C., R.Roy “A critical review on idalization and modeling for interaction among soil–foundation–structure system“ Computers and Structures. 80 (2002)1579-1594.
2. [2] Wang C.M., J.N.Reddy, K.H.Lee “Shear deformable beams and plates“ 1st Edn., Elsevier Science, Kidlington, Oxford, UK (2000).
3. [3] Basu D., N.S.V.K.Rao “Analytical solutions for Euler – Bernoulli beam on visco – elastic foundation subjected to moving load“ International Journal for Numerical and Analytical Methods in Geomechanics. 37 (2013)945- 960.
4. [4] Djondjorov P., V.Vassilev, V.Dzhupanov “Dynamic stability of fluid conveying cantilevered pipes on elastic foundations“ Journal of Sound and Vibration. 247-3 (2001) 537-546.
5. [5] Cazzani A. “On the dynamics of a beam partially supported by an elastic foundation: an exact solution-set“ International Journal of Structural Stability and Dynamics. 13 (2013)30.
6. [6] Dağlı B.Y., B.G.Sınır “Dynamics of transversely vibrating pipes under non-classical boundary conditions“ Universal Journal of Mechanical Engineering. 3-2 (2015)27-33.