Notice of Retraction Nonlinear dynamical analyses for the beam-column structure

In this paper, based on assumption that the loads acting on a beam-column structure are conservation, the Hamilton variational principle is extended to a nonlinear elastic Timoshenko-type beam-column structure located on a nonlinear elastic foundation, and the corresponding 3-dimension mathematical model for analyzing the non-linear mechanical behaviors of structure is established. As application, by using differential quadrature method and difference method, the non-linear dynamical behaviors of a non-linear elastic beam with equal cross-section and located on an elastic foundation are analyzed successfully, in which, one end of beam is fully fixed, and the other is partially fixed and subjected to an axial force. The effects of parameters on dynamic characteristic of the beamcolumn structure are considered.