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L-P Perturbation Solution of Nonlinear Free Vibration of Prestressed Orthotropic Membrane in Large Amplitude

机译：预应力正交异性膜大振幅非线性自由振动的L-P摄动解

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摘要

This paper reviewed the research on the nonlinear free vibration of pre-stressed orthotropic membrane, which is commonly applied in building membrane structures. We applied the L-P perturbation method to solve the governing equations of large amplitude nonlinear free vibration of rectangular orthotropic membranes and obtained a simple approximate analytical solution of the frequency and displacement function of large amplitude nonlinear free vibration of rectangular membrane with four edges simply supported. By giving computational examples, we compared and analyzed the frequency results. In addition, vibration mode of the membrane and displacement and time curve of each feature point on the membrane surface were analyzed in the computational example. Results obtained from this paper provide a simple and convenient method to calculate the frequency and lateral displacement of nonlinear free vibration of rectangular orthotropic membranes in large amplitude. Meanwhile, the results provide some theoretical basis for solving the response of membrane structures under dynamic loads and provide some computational basis for the vibration control and dynamic design of building membrane structures.
机译：本文综述了正交各向异性预应力正交异性膜的非线性自由振动的研究，该非线性振动常用于建筑膜结构中。我们应用L-P摄动法求解矩形正交各向异性膜大振幅非线性自由振动的控制方程，并得到简单支撑四边矩形膜大振幅非线性自由振动的频率和位移函数的简单近似解析解。通过给出计算示例，我们比较并分析了频率结果。另外，在计算实例中分析了膜的振动模式以及膜表面上每个特征点的位移和时间曲线。从本文获得的结果提供了一种简单方便的方法来计算矩形正交异性膜大振幅非线性自由振动的频率和横向位移。同时，研究结果为解决动态荷载作用下膜结构的响应提供了理论依据，为建筑膜结构的振动控制和动力设计提供了计算依据。

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  • 来源
    《Mathematical Problems in Engineering》 |2010年第3期|p.95-111|共17页
  • 作者

    Liu Chang-jiang; Zheng Zhou-Han; He Xiao-ting; Sun Jun-yi; Song Wei-ju; Xu Yun-ping; Long Jun;

  • 作者单位

    College of Civil Engineering, Chongqing University, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China,Key Laboratory of the Three Gorges Reservoir Region's Eco-Environment,Ministry of Education, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China;

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