| In this dissertation,the dynamic modeling theory of the multi-endpoint beam and the dynamic response of multibody system with multi-endpoint beams are studied based on Transfer Matrix Method for Multibody System(MSTMM).MSTMM is a new method raised by Rui to study the multibody system dynamics by using the transfer relationship between the state vectors.The state vector in this this dissertation is defined as the translational and angular accelerations as well as the internal forces and torques.The state variables can always be divided into two complementary parts and the linear relationship between these two parts can be described by the Riccati transfer equation.The Riccati transfer equation of the output end can be obtained by combing the Riccati transfer equation of the input end with transfer equation of the body element.Considering that the dimensions of the Riccati transfer equation is only half of the connection state variables,the recursive relationship of Riccati transfer equation between the input end and the output end can be directly established based on the basic equation of hinges.The Riccati transfer equation of the common hinge elements are presented,such as consolidation hinge,rotating hinge,slip hinge and virtual hinge.Compared with the new version of multibody system transfer matrix method,the method proposed can be used more wildly in tree systems without the demand of same type hinges.Both the transversal deformation of the flexible beam and the non-linear coupling term caused by transversal deformation,also known as the longitudinal shortening,are considered in the total longitudinal deformation.The floating coordinate method and assumed modes method are used to describe the deformation of flexible beam.Then the transfer equation and geometric equation of the multi-endpoint beam undergoing large motion and relatively small deformation are deduced base on Jourdan variational principle and virtual work principle.The method proposed can be used not only in the low rotational angular velocity problems,but also in the high rotational angular velocity problems.The Riccati transfer equation of multi-endpoint beam can be deduced by combing the Riccati transfer equation of the input end with transfer equation and geometric equation of the multi-endpoint beam.This dissertation enriches matrix library of MSTMM,widens the current use of MSTMM,and is instructive to establish transfer matrix of common flexible body.Several illustrative examples including hub-beam system,typical mechanical arm system and typical spacecraft system are given to validate the method proposed,to indicate the importance of an accurate model in multibody dynamics. |
