Analytical Solutions for Stochastic Vibration of Orthotropic Membrane under Random Impact Load

Orthotropic membrane materials have been applied in the numerous fields, such as civil engineering, space and aeronautics, and mechanical engineering, among others. During their serving lifespan, these membranes are always facing strong stochastic vibrations induced by the random impact load such as hail, heavy rain, and noise, among others. In this paper, the stochastic vibration problem of orthotropic membrane subjected to random impact load is investigated. The statistical characteristics of random impact load are initially obtained based on the stochastic pulse theory. Then, the Von Karman theory is applied to model the nonlinear vibration of membrane with geometric nonlinearity, which is then used to derive and solve the corresponding fokker–plank–kolmogorov (FPK). The theoretical model developed is validated by means of experiment study and monte carlo simulation (MCS) analysis. The effects of variables like pretension force, velocity of impact load, and material features on stochastic dynamic behavior of membranes are discussed in detail. This exposition provides theoretical framework for stochastic vibration control and design of membranes subjected to random dynamic load.