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A Semianalytical Method for Nonlinear Vibration of Euler-Bernoulli Beams with General Boundary Conditions

机译:具有一般边界条件的Euler-Bernoulli梁非线性振动的半解析方法

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摘要

This paper presents a new semianalytical approach for geometrically nonlinear vibration analysis of Euler-Bernoulli beams with different boundary conditions. The method makes use of Linstedt-Poincar£ perturbation technique to transform the nonlinear governing equations into a linear differential equation system, whose solutions are then sought through the use of differential quadrature approximation in space domain and an analytical series expansion in time domain. Validation of the present method is conducted in numerical examples through direct comparisons with existing solutions, showing that the proposed semianalytical method has excellent convergence and can give very accurate results at a long time interval.
机译:本文提出了一种新的半解析方法,用于不同边界条件下的Euler-Bernoulli梁的几何非线性振动分析。该方法利用Linstedt-Poincar£摄动技术将非线性控制方程转换为线性微分方程系统,然后通过使用空间域的差分正交逼近和时域的分析级数展开来寻求其解。通过与现有解决方案的直接比较,在数值示例中对本方法进行了验证,表明所提出的半分析方法具有出色的收敛性,并且可以在很长的时间间隔内给出非常准确的结果。

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  • 来源
    《Mathematical Problems in Engineering》 |2010年第speca期|p.9.1-9.17|共17页
  • 作者

    Jian-She Peng; Yan Liu; Jie Yang;

  • 作者单位

    School of Industrial Manufacturing, Chengdu University, Sichuan 610106, China;

    Department of Physics and Electronic Information, China West Normal University, Nanchong, Sichuan 637002, China;

    School of Aerospace, Mechanical and Manufacturing Engineering, EMIT University, P.O. Box 71, Bundoora, Victoria 3083, Australia;

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