﻿ 张拉平面膜结构非线性振动频率计算分析

# 张拉平面膜结构非线性振动频率计算分析Computation and Analysis for the Frequency of Nonlinear Vibration of Tensioned Plane Membrane Structure

Abstract: The nonlinear free vibration governing differential equations for the orthotropic tensioned plane membrane structure are established by Von Kármán’s membrane large deflection theory and D’Alembert’s principle. Then the governing differential equations are simplified by Bubnov-Ga- lerkin method and solved by the homotopy perturbation method (HPM), and obtained the ap-proximate analytical solution of the vibration frequency. In the computational example, the non-linear vibration frequency of the structure is computed, and the results of this paper are analyzed and compared with the exact solution. The analysis shows that the approximate analytical solution obtained in this paper is very close to the exact solution (the maximum error is less than 4%), and the approximate analytical solution obtained in this paper is more simple and convenient. This is favorable for the popularization and application in engineering.

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