Global Mode Method For Complex Flexible Strutures And Its Application In Space Composite Structures

With the needs of the national economy,the size of the flexible multibody system is increasing and the weight of the structure is becoming lighter and lighter.For example,in the field of aerospace,modern spacecrafts are often equipped with large solar wings in order to obtain sustainable energy.The elastic vibration of the solar wing is inevitably coupled with the motion of the spacecraft's main platform.The increase in the size of the solar wing will lead to a significant increase in this coupling effect.At this time,the mode of a single solar wing does not accurately reflect its elastic vibration in the system.This may leads to the lack of accuracy in the accuracy of the dynamic model obtained by using the assumed mode method.Therefore,this paper develops an analytical method that can obtain the global mode that reflects the true elastic vibration of the system,and it is applied to the dynamic modeling of flexible multibody systems.On this basis,the research on vibration control and nonlinear dynamic response is deeply carried out,which has certain theoretical significance and engineering value.In this dissertation,the complex flexible structures is taken as the research object,and an analytical method for obtaining the global mode of the system is proposed,which is applied to the dynamic modeling of the space composit beams,and its dynamic model is obtained.Based on this,some related researches have been made from the aspects of inherent characteristics,dynamic response and vibration control.The main research contents are as follows.For complex flexible structures,a general analytical method for obtaining global mode of the system is summarized.Based on the different description methods of the floating coordinate system,the strategy and steps of the system modal equation based on the global mode are described in Cartesian coordinates and Lagrange coordinates respectively.In Cartesian coordinates,the equations of motion of the system are established by using the Newton-Euler method or Hamilton principle.In the Lagrange coordinate system,the equation of motion of the system is established by using the Hamilton principle.By the partial differential equations of deformable bodies,the motion equations of rigid bodies and the matching conditions and boundary conditions describing the forces and displacements of the interface,the method of separation of variables is used to give a uniform frequency equation,the natural frequencies of the system and the global mode reflecting the real elastic vibration of the structure are obtained accordingly.Finally,the dynamic model of the system can be obtained by global mode.For flexible manipulator with flexible joints,the dynamic model based on the global mode is established by using the motion description method of Lagrange coordinates,and the dynamics and control research are carried out.First,the Hamiltonian principle is used to derive the ordinary differential equations of the rigid motion of flexible manipulator and the partial differential equations of flexible arm.The boundary conditions are used to solve the system's ordinary differential equations and partial differential equations.Then,the frequency and global mode of the system are obtained,and the orthogonalities of the global mode of the system are proved.The dynamic model of the system is obtained by the global mode.From the aspects of intrinsic characteristics and dynamic response,the dynamic model of the flexible manipulator obtained from the global mode and the assumed mode is compared and the superiority of the dynamic model obtained by the global modality is verified.Finally,based on the dynamic model obtained from the global mode,the optimal control method is used to control the flexible manipulator.For the L-shaped beam structure and the multi-beam structure connected by multiple joints,the dynamic equations are established by using the Cartesian coordinate motion description method.The global mode of the system is solved by using the boundary condition and matching condition of the system,and the orthogonality of global mode is proved.Based on this,a discrete dynamics model of the system was established.Then,compared with the finite element model,the validity and correctness of the dynamic model obtained by global mode is verified.Finally,the effects of the nonlinear stiffness,damping and friction of the joints on the dynamic response of the whole structure are discussed in the numerical analysis of the multi beam structure connected by joints.For the flexible spacecraft with a hinge connected solar wing,the dynamic equations are established by using the Cartesian coordinate motion description method.By using the boundary conditions and matching conditions of the system,the natural frequencies and the global modes of the flexible spacecraft are solved,and the orthogonality of the global mode of the system is proved.The nonlinear dynamic model of the system is established by considering the nonlinear stiffness,damping and friction of the joints.By comparing the frequency with the finite element model,the validity and correctness of the dynamic model obtained by the global mode is verified.In the subsequent analysis of the inherent characteristics of the system,the influence of flexible vibration of flexible solar wings on the rigid body position and attitude of flexible spacecraft is discussed.Finally,the dynamic response of the system is analyzed,and the influence of joint parameters on the dynamic response of spacecraft orbit maneuver and attitude adjustment is studied.