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A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions

机译：修正的傅里叶级数解在一般边界条件下截顶圆锥壳的振动分析

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摘要

Free vibration analysis of truncated conical shells with general elastic boundary conditions is presented in this paper. An accurate modified Fourier series solution is developed, in which, regardless of the boundary conditions, each displacement of the conical shell is invariantly expressed as a new form of improved series expansions composed of a standard Fourier series and closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series expansion. All the expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz method. By using the present method, conical shells with arbitrary boundary conditions including all classical and elastic end restraints can be solved in a unified form. The accuracy and convergence of the current approach are validated by numerical examples and comparison with FEM results and those from the literature, and excellent accuracy is demonstrated. Comprehensive studies on the effects of elastic restraint parameters, semi-vertex angle and the ratio of length to radius are also reported. Some new results are presented for cases with elastic boundary restraints which may serve as benchmark solution for future researches.
机译：提出了具有一般弹性边界条件的截顶圆锥壳的自由振动分析。开发了一种精确的改进傅里叶级数解，其中，不管边界条件如何，圆锥形壳的每个位移都始终表示为改进级数展开的新形式，该级数由标准傅里叶级数和封闭形式的辅助函数组成，以确保并加快了系列扩展的收敛速度。所有的膨胀系数都被当作广义坐标，并使用瑞利-里兹方法确定。通过使用本方法，可以以统一的形式求解具有任意边界条件的圆锥形壳，包括所有经典的和弹性的端部约束。通过数值算例验证了该方法的准确性和收敛性，并与有限元分析结果和文献中的结果进行了比较，并证明了优异的准确性。还报道了关于弹性约束参数，半顶点角和长度与半径之比的影响的综合研究。对于具有弹性边界约束的情况，提出了一些新结果，可以作为未来研究的基准解决方案。

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  • 来源
    《Applied Acoustics》 |2014年第11期|82-96|共15页
  • 作者

    Guoyong Jin; Xianglong Ma; Shuangxia Shi; 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;

    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

    Free vibrations; Truncated conical shells; General end restraints; Series solution;

    机译：自由振动;截锥形的外壳;一般终端约束;系列解决方案;

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