Free vibration analysis of cylindrical shells using the Haar wavelet method
Free vibration analysis of cylindrical shells using the Haar wavelet method
复制标题
使用 Haar 小波方法进行圆柱壳的自由振动分析
DOI：
10.1016/j.ijmecsci.2013.09.025
复制
发表时间：
2013-12
影响因子：
7.3
通讯作者：
Zhigang Liu
中科院分区：
文献类型：
--
作者：
Xiang Xie;Guoyong Jin;Zhigang Liu
本文利用Haar小波离散化方法，对各种边界条件下圆柱薄壳的自由振动问题提出了一种新的有效的解法。采用Goldenveizer-Novozhilov壳理论建立理论模型。控制方程中的位移及其导数在轴向用Haar小波级数及其积分表示，在周向用Fourier级数表示。积分过程中出现的常数由边界条件确定，从而将偏微分方程转化为一组代数方程。通过求解代数方程组，得到了圆柱壳的频率参数。通过与文献中的数值结果进行比较，验证了本文的解。观察到非常一致。结果表明，用少量的配点就可以得到精确的频率参数，边界条件也很容易得到。该方法具有计算简单、收敛速度快、计算量小、精度高等优点。
This paper presents a novel and efficient solution for free vibrations of thin cylindrical shells subjected to various boundary conditions by using the Haar wavelet discretization method. The Goldenveizer–Novozhilov shell theory is adopted to formulate the theoretical model. The displacements and their derivatives in the governing equations are represented by Haar wavelet series and their integrals in the axial direction and the Fourier series in the circumferential direction. The constants appearing from the integrating process are determined by boundary conditions and thus the partial differential equations are transformed into a set of algebraic equations. The frequency parameters of the cylindrical shells are obtained by solving the algebraic equations. The present solution is verified by comparing the numerical results with those previously published in literature. Very good agreement is observed. It is shown that accurate frequency parameters 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, low computational cost and high precision.
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影响因子：
8.4
作者：
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通讯作者：
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影响因子：
1.6
作者：
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DOI：
10.1016/j.camwa.2008.05.005
发表时间：
2008-11
期刊：
Comput. Math. Appl.
影响因子：
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作者：
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通讯作者：
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DOI：
10.1016/j.mcm.2011.07.006
发表时间：
2011-12
期刊：
Math. Comput. Model.
影响因子：
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作者：
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通讯作者：
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