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

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.

Nonlinear vibration of an orthotropic moving membrane

“…where N y , N x , N yx and N xy represent the internal forces of a membrane at each unit length. The membrane is an orthotropic material, and one can obtain 20,21 :…”

“…The effect of preload, radius and impact velocity on the reliability of structure were also examined in Refs. [19,20]. They also considered the coupling between different modes and analysed free vibrations of orthotropic membranes in.Ref.…”

Effect of Geometric Nonlinearity on Membrane Roof Stability in Air Flow

“…Equation ( 27) is a strongly nonlinear vibration equation. For different equations of strongly nonlinear vibration, many scholars have studied the corresponding solutions [13][14][15][16][17]. In this paper, we propose the improved multiscale method based on the principle of modified Lindestedt-Poincaré method to solve equation (27).…”

Hailstone-induced dynamic responses of pretensioned umbrella membrane structure

“…Liu et al (2018a) investigated the nonlinear damped vibration of pretensioned planar rectangular orthotropic membrane structure under impact load through analytical, experimental, and numerical methods. Li et al (2017, 2018) studied stochastic vibration of planar rectangular orthotropic membrane structure under impact load theoretically and experimentally. Zheng et al (2019) investigated the dynamic response of planar rectangular orthotropic membrane structure excited by the heavy rainfall by analytical and experimental methods.…”