Research On Dynamic Modeling And Vibration Control Of Polygonal Composite Beam Structure

The truss structure of the ring antenna is the supporting structure of the large deployable ring antenna,and its dynamic behavior has a great influence on the pointing accuracy of the satellite antenna.The research on the inherent characteristics,dynamic response and active control of the ring truss structure will be of great significance to the development of the satellite.In this paper,the ring truss structure is simplified to a polygonal composite beam structure,the global modal method is used to solve the global mode of the polygonal composite beam structure,and the discrete dynamic equation is obtained by using the continuous displacement of the analytical global modal discrete system.The active vibration control of the structure is studied by piezoelectric actuator.The dynamic modeling,natural characteristic analysis and dynamic response analysis are carried out for the out-of-plane vibration of polygonal composite beam structure.The out-of-plane bending vibration and torsional vibration of each beam are considered.According to the matching relations of bending displacement,rotation angle,torsion angle,shear force,bending moment and torque and the boundary conditions of the system,the frequency equation of the system is obtained.furthermore,the natural frequency and analytical global mode of the system are obtained.According to the matching conditions and boundary conditions of the system,the orthogonality of the global modes of the system is proved,and the modal mass and modal stiffness of the system are obtained.The results of numerical examples show that the natural frequencies and modal shapes obtained by the global modal method and the finite element method are in good agreement,indicating that the global modal method can be used to obtain the global modes of out-of-plane vibration of polygonal composite beam structures.and the global modal model is accurate.Through the discretization of the global mode to the displacement,the discrete dynamic equation of the system is obtained,and the principle of mode selection when describing the out-of-plane vibration of polygonal composite beam structure is determined.The dynamic modeling and inherent characteristic analysis are carried out for the spatial motion of the polygonal composite beam structure with supporting beam.The axial vibration,torsional vibration and bending vibration in two directions of each beam are considered.According to the matching relations of axial displacement,bending displacement,rotation angle,torsion angle,axial force,shear force,bending moment and torque of each beam and the boundary conditions of the system,the frequency equation of the system is obtained,and then the natural frequency and analytical global mode of the system are obtained.According to the matching conditions and boundary conditions of the system,the orthogonality of the global modes of the system is proved,and the modal mass and modal stiffness of the system are obtained.The results of numerical examples show that the natural frequencies and modal shapes obtained by the global modal method are in good agreement with those obtained by the finite element method,indicating that the global modal method can be used to obtain the global modes of spatial composite beam structures.and the global modal model is accurate.The piezoelectric active control for the polygonal composite beam structure are carried out.The control torque of the system is obtained by piezoelectric ring,and the control equation of piezoelectric intelligent polygonal composite beam structure is established.The active vibration control of quadrilateral composite beam structure is simulated by using LQR control method,and the simulation results show that the control effect is good.The influence of different number of piezoelectric actuators on the control effect is analyzed.The simulation results show that when the number of piezoelectric actuators reaches a certain number,the change of control effect will not be obvious with the increase of the actuator.