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This paper studies the calculation method about the displacement response mean function of rectangular orthotropic membranes with four edges fixed under stochastic impact loading. We set up the nonlinear stochastic governing differential equation, solve it according to the perturbation method and the random vibration theory and obtain the displacement response mean value function of the membrane surface. Furthermore, this paper makes a random simulation test for ZZF membrane material which is commonly applied in the membrane structural engineering and obtains abundant deflection response sample curves about the feature points of the membrane surface. For sample curves statistical analysis at some fixed time, sample means can be obtained, which verify the correctness of the theoretical calculation method. The calculation method provides a theoretical basis for vibration control of building membrane structures to control the occurrence of natural disasters.
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