Abstract
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.
Highlights
Orthotropic membranes are lightweight, flexible structural elements used in numerous applications in construction building, space and aeronautics, and mechanical engineering, among others [1,2]
When the energy of random impact load is limited to only being able to induce weak stochastic vibration occurring at the edge region, such as Point A1, Point A2, and Point C, the probability density function (PDF) curve of displacement will approximate the Gaussian distribution, which may suggest the function of membrane as the linear filter system
Impact load is limited to only being able to induce weak stochastic vibration occurring at the edge region, such as Point A1, Point A2, and Point C, the PDF curve of displacement will approximate the Gaussian distribution, which may suggest the function of membrane as the linear filter system
Summary
Orthotropic membranes are lightweight, flexible structural elements used in numerous applications in construction building, space and aeronautics, and mechanical engineering, among others [1,2]. The impact load in nature, such as pulse wind, hails, and explosion, among others, generally possesses uncertain characteristics [14], which will lead to the stochastic vibration with larger deformation for membrane. In this case, the actual deformation of membrane can exceed the prediction of analytical results based on the deterministic vibration theory, and increase their risk of collapse in use. The present analytical model could not provide a reliable solution from probabilistic and statistical viewpoints It is worth purposing the stochastic vibration model of membrane subjected to uncertain impact load. The effects of pretension force, velocity of impact load, and membrane material on stochastic vibration behavior are discussed
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