Buckling and Free Vibration of a Single Pile Considering the Effect of Soil–Structure Interaction

The buckling response and free vibration characteristics of a single pile in the elastic foundation are investigated. Considering the effect of soil–structure interaction and geometric nonlinearity, the nonlinear equation of motion for a single pile is derived by Hamilton’s principle. Then, closed-form solutions of the critical load and buckled configuration of the pile are obtained analytically, and the natural frequencies of the pre- and post-buckling pile are examined. Finally, the effect of elastic foundation parameter on the critical load of the pile is discussed, and the effect of axial load on the natural frequencies of the pile is also explored. Numerical results show that the effect of elastic foundation parameter plays a dominant role on the critical load and buckled configuration of the pile, and the shear parameter affects the critical load directly. The axial load effect on the dynamic characteristics of the pre-buckling pile is significant, meanwhile, it may contribute very small to the post-buckling pile when the axial load exceeds some specific values.