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Open AccessArticle

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

by Dong Li 1,2, Zhou-Lian Zheng 1,2,3,*, Rui Yang 1 and Peng Zhang 1
1
Scholl of Civil Engineering, Chongqing University, Chongqing 400045, China
2
Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
3
Chongqing Jianzhu College, Chongqing 400072, China
*
Author to whom correspondence should be addressed.
Materials 2018, 11(7), 1231; https://doi.org/10.3390/ma11071231
Received: 11 June 2018 / Revised: 12 July 2018 / Accepted: 13 July 2018 / Published: 18 July 2018
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. View Full-Text
Keywords: orthotropic membrane; random impact load; stochastic vibration; geometric nonlinearity; FPK method orthotropic membrane; random impact load; stochastic vibration; geometric nonlinearity; FPK method
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Li, D.; Zheng, Z.-L.; Yang, R.; Zhang, P. Analytical Solutions for Stochastic Vibration of Orthotropic Membrane under Random Impact Load. Materials 2018, 11, 1231.

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