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An analytical study of the non-linear vibrations of functionally graded cylindrical shells subjected to thermal and axial loads

机译：功能梯度圆柱壳在热和轴向载荷作用下的非线性振动分析研究

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摘要

An analytical method and a new simplifying model of FG (functionally graded) cylindrical shells are presented based on Hamilton's principle, Von Karman non-linear theory and the first-order shear deformation theory, and subjected to thermal and axial loads. The coupled non-linear partial differential vibration equations are discretized based on a series expansion of linear modes and a multiterm Galerkin's method. Neglecting the membrane inertias and rotary inertias, the equation of motion is transformed into a reduced equation in the generalised transverse displacement. Adopting multiple scales method, the amplitude frequency dependence and the non-linear forced frequency response are obtained in the case of a single mode assumption. The good agreement found was very satisfactory, in comparison with previous theoretical approaches. The purpose of this approach was to provide engineers and designers with an easy method for determining the non-linear vibration behaviour of FG cylindrical shells.
机译：基于汉密尔顿原理，冯卡曼非线性理论和一阶剪切变形理论，提出了FG（功能梯度）圆柱壳的解析方法和简化模型，并对其进行了热载荷和轴向载荷研究。基于线性模式的级数展开和多项Galerkin方法，离散了耦合的非线性偏微分振动方程。忽略膜惯性和旋转惯性，将运动方程转化为广义横向位移中的简化方程。采用多尺度方法，在单模假设的情况下，获得了振幅频率依赖性和非线性强迫频率响应。与先前的理论方法相比，发现的良好协议非常令人满意。这种方法的目的是为工程师和设计人员提供一种简便的方法来确定FG圆柱壳的非线性振动行为。

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  • 来源
    《Composite Structures》 |2013年第3期|261-268|共8页
  • 作者

    G.G.Sheng; X. Wang;

  • 作者单位

    School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha, Hunan 410114, People's Republic of China;

    School of Naval Architecture, Ocean and Civil Engineering (State Key Laboratory of Ocean Engineering), Shanghai Jiaotong University, Shanghai 200240, People's Republic of China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    functionally graded; cylindrical shell; non-linear vibration; multiple scales method;

    机译：功能分级;圆柱壳非线性振动多尺度法;

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