To meet the needs of large space telescopes, such as light weight, high folding ratio, and low manufacturing cost, a flexible deployable regular hexagonal membrane sunshield is proposed in this paper. Firstly, the dynamic equation of the membrane plane is established by the micro-element method. Then, the response surface method is used to obtain the mathematical model of the fundamental frequency of the membrane sunshield. The factors influencing this model, such as the corner pulling force, the effective circle radius, and the edge arch height, are analyzed. By combining the formula of the fundamental frequency of the membrane sunshield and the effective area ratio of the sunshield, the multi-objective optimization function of the fundamental frequency of the membrane sunshield is obtained. A scaled-down experimental prototype of the membrane sunshield is built, and the modal test is performed on the thin membrane plane with a circular fixed boundary in the middle. Comparing the experimental results with the finite element simulation results, the mode shape and the fundamental frequency are highly consistent. This proves that the model can be used to solve the fundamental frequency of the membrane sunshield under the same boundary.
Keywords: dynamics; fundamental frequency; membrane sunshield; modal test.