Transient Response Beam Buried Partly in a Nonlinear Foundation

Abstract

This paper presents a mathematically exact solution of the continuum to the transient response of a vertical single beam buried partly in a nonlinear foundation because of a support displacement. The foundation has a nonlinear property between reaction and displacement similar to elastoplastic foundation and viscous damping of the Voigt type. Winkler’s hypothesis can be produced from the relative displacement based on a foundation displacement, which may be imitated by behavior of a one-dimensional shear wave in the medium. The approach, which involves the classical beam theory and the method of eigenfunction expansion, is simple and clear for seeking solutions and solving equations of motion under the boundary and initial conditions. The connection conditions on the mechanics at the interface and the continuity for displacement and its velocity at the changing time are effectively applied to the relationship between the governing equations of motion satisfied in an elastic domain and those satisfied in a plastic domain.