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Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method

机译：使用Haar小波方法分析功能梯度圆锥壳和环形板的自由振动

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摘要

The main aim of this paper is to provide a simple yet efficient solution for the free vibration analysis of functionally graded (FG) conical shells and annular plates. A solution approach based on Haar wavelet is introduced and the first-order shear deformation shell theory is adopted to formulate the theoretical model. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. The separation of variables is first performed; then Haar wavelet discretization is applied with respect to the axial direction and Fourier series is assumed with respect to the circumferential direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. Then natural frequencies of the FG shells are obtained by solving algebraic equations. Accuracy and reliability of the current method are validated by comparing the present results with the existing solutions. Effects of some geometrical and material parameters on the natural frequencies of shells are discussed and some selected mode shapes are given for illustrative purposes. It's found that accurate frequencies can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. The advantages of this current solution method consist in its simplicity, fast convergence and excellent accuracy.
机译：本文的主要目的是为功能梯度（FG）圆锥形壳体和环形板的自由振动分析提供一个简单而有效的解决方案。介绍了一种基于Haar小波的求解方法，并采用一阶剪切变形壳理论建立了理论模型。假定壳的材料特性根据一般的四参数幂律分布在厚度方向上连续变化，以组分的体积分数表示。首先执行变量分离；然后在轴向上应用Haar小波离散化，并在圆周方向上采用傅里叶级数。积分过程中出现的常数是由边界条件决定的，因此偏微分方程被转换为代数方程。然后通过求解代数方程获得FG壳的固有频率。通过将当前结果与现有解决方案进行比较，可以验证当前方法的准确性和可靠性。讨论了一些几何和材料参数对壳体固有频率的影响，并出于说明目的给出了一些选定的模式形状。发现通过使用少量的配置点可以获得准确的频率，并且可以轻松实现边界条件。当前解决方案方法的优点在于其简单，快速收敛和出色的准确性。

著录项

  • 来源
    《Applied Acoustics》 |2014年第11期|130-142|共13页
  • 作者

    Xiang Xie; Guoyong Jin; Tiangui Ye; Zhigang Liu;

  • 作者单位

    College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, PR China;

    College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, PR China;

    College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, PR China;

    College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, PR 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

    Haar wavelet series; Conical shells; Annular plates; Free vibrations;

    机译：Haar小波系列;锥形壳;环形板;自由振动;

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