Membrane Deflection And Modal Analysis Based On Circular Uniform Support

With the development of science and technology,in order to meet the needs of space detection and other aspects,it is necessary to establish a large aperture,high-resolution space optical imaging system.However,with the increase of telescope aperture,the weight of telescope will also rise sharply,which will lead to higher requirements on parts processing,structure control and rocket carrying capacity,even beyond the technical capacity.The diffractive thin film telescope uses the thin film material as the main mirror base of the optical system,which has the characteristics of thin thickness and small density for the large aperture imaging system,and can effectively reduce the overall weight of the system,so the diffractive thin film imaging technology has become a very effective means to solve this problem.For the application of diffractive films,mechanical analysis is a very important research direction.Because of the particularity of membrane flexible body,its structural rigidity is determined by its shape and prestress,which leads to the particularity of its mechanical analysis.In this paper,the film force characteristics are analyzed.The main contents are as follows:1: This paper introduces the background and significance of the project,investigates the theory of large deflection of thin film,the current situation of membrane vibration model at home and abroad,and the measurement method of membrane plane stress,expounds the necessity of mechanical analysis of diffractive membrane main mirror,as well as the difficulties and method analysis of measurement of membrane prestress.2: Based on the large deflection theory of circular membrane and the vibration model,the influence of membrane prestress,radius,external load and other parameters on the mechanical properties of the membrane is calculated,and its specific variation law is analyzed.It provides theoretical basis for the application of thin film in practice.3: The model of membrane element and shell element in ABAQUS finite element software is established,and the parameters of membrane prestress,radius and external load are changed for analysis and simulation.The model of membrane element and shell element in ABAQUS finite element software is established for simulation,and compared with the calculation results of theoretical model,and the mutual verification is completed.Furthermore,the correctness of the theoretical model and the relationship between the mechanical properties of the films and the parameters of the films are determined.4: In the early stage,the relationship between membrane center deflection,uniform load and membrane prestress is analyzed by theoretical equation and finite element method,and the corresponding equation is established.Because it is difficult to measure the membrane stress,the theoretical equation and finite element simulation can be used to calculate the membrane prestress by measuring the membrane center deflection and uniformly distributed load.Based on this principle,the corresponding experiments are designed and the theoretical analysis is carried out,which verifies the correctness of the theoretical model and the feasibility of using the method of measuring displacement to calculate the prestress.