Research On The Model Updating Methods Of Nonlinear Dynamic Model Of Jointed Structures

With the rapid development of space industry,in order to meet the needs of space missions like deep space exploration,earth observation,space station construction and so on,large deployable structures with joints,such as bracing structure of deployable antennas and supporting deployable mast of solar arrays,are widely used.Deployable structures are connected by a lot of joints,in which clearance often exists.Nonlinear phenomena such as friction and impact occurs for the joint clearance,which have a bad effect on the accuracy and resistant capacity to interference.The dynamic models of jointed structures can generally be divided to two types:linear models and nonlinear models.In order to facilitate the analysis and calculation,in the spacecraft engineering design,the joint is often simplified as a linear beam element or linear spring unit.This engineering approach ignores the non-linear effect of the hinge,which may bring larger errors to in the refined dynamics modeling of the system.Therefore,it is very necessary to establish the nonlinear model of the jointed structures which takes the nonlinearities of joints into consideration.The main work of this thesis is as follows.The common solutions of system dynamics differential equations are introduced in details,including methods in both time domain and frequency domain.The common numerical methods for solving the time domain response is the direct integration method,including the central difference method,Wilson-θ method,Houbolt method and Newmark-β method.Derivation process of each method is introduced and ideas of programing each method is summarized in tables.The basic theory of harmonic balance method,which is a wildly-used method in frequency domain,is introduced.These methods provide a theoretical basis and technical means for later research.The nonlinear dynamic model of a cantilever beam jointed by two nonlinear joints is established.The nonlinear dynamic responses in both time domain and frequency domain of the structure is calculated with taking three different nonlinear characteristics into account,respectively,such as cubic nonlinearity,non-linearity of gap and non-linearity of piecewise stiffness.In the time domain,the nonlinear dynamic response is calculated with the central difference method and the Newmark-β method.Two results shows consistency which means the correctness of the calculation.In the frequency domain,the frequency response analysis of the structure is carried out by the harmonic balance method and the natural frequency of the structure is obtained which is verified by the time domain results.This demonstrates that the harmonic balance method is practical method to analyze the nonlinear structure.A one-bay plane truss model with cubic nonlinear joint is established.The frequency response function is calculated using the harmonic balance method.The single truss model is modified based on the frequency response function which results verify the effectiveness of the pattern-search method.Taken joints as nonlinear springs,the nonlinear model of rod with a joint at each end is established and the equivalent stiffness of the whole rod is deduced considering the stiffness only in axial direction.The model of jointed structures is then established on this.The dynamic simulation of the jointed truss is carried out and the time-domain dynamic response is calculated by using the Newmark-β method considering three different nonlinear model of the joint.The influence of different factors on the dynamic response trusses was analyzed.