Research On Coupling Dynamic Characteristics Of Planar Membrane Structure

With the development of the aerospace industry,various aerospace missions have placed higher requirements on the organization structure and working performance of the spacecraft.The membrane structure has been widely used by research scholars because of its advantages of light weight,foldability,and high storage ratio.The membrane structure working on the rail cannot avoid vibration.The actuator for vibration suppression is generally installed on the frame.In order to suppress the vibration of the membrane,it is necessary to understand the conditions of the coupled vibration of the membrane structure.Researchers have mostly studied the critical point of coupled vibration of membrane structures only at the stage of simulation analysis or simplified the coupling.Therefore,In this paper,we will take the unilaterally fixed planar membrane structure as the research object,and study the coupling dynamic characteristics of the planar membrane structure.The dynamic model of damped and undamped free vibration of the supporting frame was established by the modal synthesis method of fixed interface.The supporting frame was regarded as a continuous system composed of continuously distributed mass,spring and damping.The mass matrix,stiffness matrix of the supporting frame and the first-second natural frequency and vibration function expression of the supporting frame are derived;the influence of each parameter of the supporting frame on its fundamental frequency is analyzed,and finally the modal simulation analysis is carried out on the supporting frame.The simulation results validate the theoretical analysis.The damped and undamped linear free vibration characteristics of rectangular membrane are analyzed.The linear free vibration fundamental frequency expression and vibration function of the membrane are obtained.The influence of the membrane parameters on the linear fundamental frequency is analyzed.The influence of damping on the linear free vibration characteristics of the membrane is analyzed in time domain and frequency domain respectively;The damped and undamped nonlinear free vibration characteristics of the rectangular membrane were analyzed.The expressions of first-order and arbitrary-order approximate nonlinear fundamental frequencies and vibration functions including frequency doubling terms are derived,and the effects of various membrane parameters on the nonlinear fundamental frequency of the membrane are analyzed;The main manifestations of the membrane nonlinearity is analyzed.The effects of damping,initial displacement and membrane prestress on the nonlinear free vibration characteristics of the membrane,and the relationship between the linear fundamental frequency and the nonlinear fundamental frequency is analyzed.The dynamic model of free vibration coupling of the planar membrane structure is established by the modal synthesis method with fixed interface;the coupling mass matrix and the coupling stiffness matrix of the planar membrane structure are derived,the expression of the free vibration coupling fundamental frequency of the planar membrane structure is derived.The influence of the parameters of membrane structure on the coupling fundamental frequency is analyzed;the vibration characteristics of the frame considering the prestress of the membrane are analyzed,and the modal expansion of the amplitude-frequency response matrix of the forced vibration of the frame is derived;Combined with the previous research on the vibration characteristics of the frame and the membrane.The coupling dynamic characteristics of the planar membrane structure are analyzed,and the conditions of the coupling vibration between the frame and the membrane are analyzed;the dimensionless analysis of the membrane structure is performed to obtain the similarity criteria of the parameters between the membrane structure model and the physical object;The structure was analyzed by modal simulation,and the coupling dynamic characteristics of the membrane structure were reflected in the change of vibration mode and the theoretical analysis was verified.