Research On Nonlinear Effect Of Free Vibration Of Membrane Structures In Space

The space membrane structure has the advantages of low quality and high folding ratio,and has a good application prospect in space detection.The main load on the rail is the pulse load generated during the track maintenance,the thermal deformation load generated by the entrance and exit,and then the free-attenuation vibration is performed under the load,so it can be regarded as the free vibration of the given initial displacement.The membrane needs to provide bending stiffness by applying tension.In the process of free vibration,when the initial displacement is small,the tension change is negligible,and it belongs to linear free vibration with no change in stiffness;when the initial displacement is large,the tension change is not negligible.The nonlinear vibration phenomenon in which the stiffness changes with the tension changes,which changes the dynamic characteristics of the membrane structure.Therefore,it is necessary to study the nonlinear free vibration of the membrane structure.The rigidity of the frame providing tension and support is generally much larger than that of the membrane.The boundary of the membrane can be regarded as a rigid boundary.Therefore,the rectangular membrane with solid surrounding is considered as the research object,and the dynamic characteristics of the free vibration of the membrane structure are studied.Firstly,the nonlinear effect of free vibration of thin membrane structure is studied and analyzed from the perspective of theoretical analysis.By establishing the free vibration partial differential dynamics model under the continuous system and considering the nonlinear effects caused by the tension variation,the first-order and second-order approximate theoretical solutions of the nonlinear free-vibration fundamental frequency of the membrane structure are derived and the corresponding high-orders are included.The expression of the vibration function of the membrane structure of the harmonic term is obtained by the relationship between the initial displacement and the dynamic characteristics of the membrane structure.On this basis,the damping coefficient is introduced to analyze the nonlinear vibration phenomenon of the membrane structure under the condition of damping,and the difference between nonlinear vibration and linear vibration is obtained.According to the first-order approximate solution of the fundamental frequency of nonlinear free vibration,a nondimensional dynamic model is established,and the conditions of similar dynamics between thin membrane structures of the same material but different sizes are derived.According to the nonlinear dynamic model,the linear application criterion is established under the condition of given acceptable error,which provides a basis for the determination of the membrane structure selection method.Secondly,the nonlinear effects are studied from the perspective of simulation analysis.The free vibration of the membrane structure was analyzed by establishing a thin membrane structure simulation model and using a nonlinear analysis method.By applying different initial displacements and analyzing the response curve,the nonlinear free vibration characteristics of the fundamental frequency with tension can be obtained under the condition that the tension of the membrane is not negligible,which is in good agreement with the theoretical analysis..The accuracy of the dimensionless model and the linear applicable criterion was verified by changing the structural parameters of the membrane.Aiming at the ground verification of the membrane structure,the nonlinear effect of the free vibration of the membrane structure under air environment is simulated and analyzed,and the influence of air on the free vibration of the membrane structure is analyzed.Finally,the nonlinear effects are studied from the perspective of experimental analysis.Based on the results of theoretical analysis and simulation analysis,the corresponding experimental schemes are designed to carry out the free vibration test of thin membrane structures in both atmospheric and vacuum environments.The experimental results show that the membrane structure exhibits obvious nonlinear vibration phenomenon under the condition that the tension is not negligible,and it has good consistency with the theoretical analysis results and the results of simulation analysis.