Modeling And Analysis Of Nonlinear Dynamics For Joint And Deployable Structure

Deployable structures which are employed as large space supporting arms and supporting structures of space-borne antennas are widely used in manned spaceflight and earth observation space missions due to their large stiffness, small folding volume, light weight, and easy extensibility. With the development of our national defense, the requirements of the characteristics related with the dynamic capacity of deployable structures are improved, such as accuracy after deploying and resistant capacity to interference. So dynamic research on deployable structures is of great importance for the design, analysis, and capacity improvement of such structures.Taking revolute joints and spherical joints as research objects, the nonlinear stiffness and damping caused by clearance, contact, and impact in radial and lateral directions of the joint are investigated. The nonlinear contact model for joint contact in radial direction is established based on the experience formula and constraints of contact, which is verified by experiments. Based on the natural frequency expression for joints with clearance, the dynamic stiffness of joints in radial direction is built. Dynamic model of revolute joint in lateral direction is established to deduce the damping ratio caused by friction and impact. The effects of preload, clearance, and stiffness on damping ratio are analyzed, which are verified by experiments. The research on the stiffness and damping of joints is beneficial for high accuracy dynamic analysis and design of deployable structures.Based on the dynamic analysis method which is the superposition of transient deformation and modal synthesis method, the modal transfer matrix for different characteristics of structures is deduced for dynamic analysis of jointed structure. Taking single jointed beam as the study object, the analysis for the effect of the stiffness of joints on the natural frequency and mode shape of the jointed beam is conducted basing on the mode theory and boundary constraints. The natural frequency and mode shape of double beams with a joint are deduced to analyze the impact response of the beams. Besides, the impact model for jointed link in radial direction is established. The analysis and experiment for the impact response of jointed link are taken.Considering the stiffness and damping of the joint in the bend direction of a beam, a linear dynamic model for a jointed beam is established. And the effects of the number and the stiffness of joints on the natural frequency and mode shape are investigated. The harmonic transfer expression for the nonlinear force of joint is introduced to analyze the effects of the parameters of joint on the natural frequency of joints. The nonlinear jointed beam model is built to analysis the effect of the clearance and stiffness of joints and excitation force on the dynamic characteristics of the jointed beam. By solving the path of natural frequencies, the effect surface of the number, location, and stiffness of joints on the limitation of natural frequency of jointed beams is obtained. The effect function of the joint parameters on the natural frequency is established. The method and results for the jointed beam can be expanded in dynamic analysis of complex jointed structure. It can be a reference of the design and analysis of deployable structures.The dynamic model of deployable structures is established by introducing the joint model. Basing on central difference method, additional force method is proposed for the dynamic analysis of the nonlinear multi-degrees structure. The effects of the joint clearance, excitation force, and friction on the natural frequency and the dynamic response of deployable structures are obtained. The dynamic analysis of deployable structures with joints is conducted. The effect of the parameters of joints and the excitation condition on the structure is analyzed. The experiment for the deployable structure is conducted to verify the dynamic model. Considering the nonlinear characteristic of joint and cable, the dynamic model for jointed structure with cable is built. The effect of the parameters on the structure is investigated by ploting the phase diagram.For obtaining the dynamic response of jointed structures in high frequency exaction to satisfy the need of dynamic analysis of large deployable structures, the frequency domain stiffness and mass matrices are proposed. The matrices are established based on the Fourier transform of the longitudinal wave equation and transverse wave equation. The matrices are verified by comparing the natural frequency results of a link which are obtained by the theoretical equation, finite element method, and frequency domain matrices. Basing on the equivalent principle of equal stress energy and equal node displacement, the equivalent model for trusses is built and verified by comparing common finite element and frequency domain matrices. When the number of the period element is less than11, the error of equivalent model of the truss in plane is less than14%, and the error of equivalent model for the truss out of plane is less than7%. The equivalent model for truss is verified. The cubic spring model for joint is introduced into the deployable model. The analysis for deployable structures found that the larger the coefficient of the stiffness of the joint is, the more rapidly the natural frequency increases. The effect model for the natural frequency of deployable structures is established by fitting the analysis results.