Abstract: In this paper,based on the Hamilton'sprinciple, a consistent linear dynamic model in con-tinuous form of a general flexible body is derived.Tile finite dimensions dyllalnic equations considering the effect of the coupling of rigid motion andelastic vibratiolls is obtailled by using mode sumption method. This research explains the phe-nomenon of dynamic stiffening due to the couplingbetween rigid motion and elastic deflection. Thevalidity of the theories presented in this paper isverified by a numerical sim...