The finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagranges equations. The second order coupling terms between rigid large overall motion, arc length stretch, lateral flexible deformation kinematics and torsional deformation terms are included in the present exact coupling model to expand the theory of one-order coupling model. The dynamic response of the present model is compared with that of zero-order approximate model and one-order coupling model. Then the changes of dynamic stiffening terms due to the new coupling terms are discussed according to different models. At the same time, the effect of initial static deformation in the tip is considered to study the vibrant deformation of flexible beam. The difference between zero-order approximate model, one-order coupling model and the present exact model is revealed by the frequency spectrum analysis method and it is concluded that the speed of overall motion is a vital cause for the difference between different models. And we found that the dynamic stiffening phenomenon still exists in rigid-flexible coupling system while the overall motion is free. But the effect of dynamic stiffening in the present exact model is not as severe as that in the one-order coupling model.