Calculating the forced response of cylinders and cylindrical shells using the wave and finite element method
Calculating the forced response of cylinders and cylindrical shells using the wave and finite element method
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DOI：
10.1016/j.jsv.2014.04.042
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发表时间：
2014-10
影响因子：
4.7
通讯作者：
J. Renno;B. Mace
中科院分区：
文献类型：
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作者：
J. Renno;B. Mace
在极少数(和简单的)情况下，圆柱体的动力响应可以解析地得到。对于复杂的(厚的或各向异性的)圆柱体，研究人员通常采用有限元方法。这可能会导致大型模型，特别是在更高的频率下，这会转化为高计算成本和内存要求。本文用波动和有限元方法求解轴向均匀圆柱体(可以通过厚度任意复数)的响应。利用圆柱体沿圆周和轴向的均匀性，利用周期结构理论对圆柱体矩形小段的有限元模型进行后处理，得到圆柱体的波动特性。利用有限元方法的全部功能，可以得到小节段的有限元模型。然后，将圆柱体的受迫响应假定为逆傅立叶变换。然而，由于闭合圆柱体周围有整数个波长，傅里叶逆变换中的一个积分就变成了一个简单的求和，而另一个积分可以用轮廓积分和留数定理来解析求解。其结果是一种计算效率高的技术，用于获得对任意复杂厚度的轴向均匀圆柱体的时间简谐、任意分布载荷的响应。
The dynamic response of circular cylinders can be obtained analytically in very few (and simple) cases. For complicated (thick or anisotropic) circular cylinders, researchers often resort to the finite element (FE) method. This can lead to large models, especially at higher frequencies, which translates into high computational costs and memory requirements. In this paper, the response of axially homogenous circular cylinders (that can be arbitrarily complex through the thickness) is obtained using the wave and finite element (WFE) method. Here, the homogeneity of the cylinder around the circumference and along the axis are exploited to post-process the FE model of a small rectangular segment of the cylinder using periodic structure theory and obtain the wave characteristics of the cylinder. The full power of FE methods can be utilised to obtain the FE model of the small segment. Then, the forced response of the cylinder is posed as an inverse Fourier transform. However, since there are an integer number of wavelengths around the circumference of a closed circular cylinder, one of the integrals in the inverse Fourier transform becomes a simple summation, whereas the other can be resolved analytically using contour integration and the residue theorem. The result is a computationally efficient technique for obtaining the response to time harmonic, arbitrarily distributed loads of axially homogenous, circular cylinders with arbitrary complexity across the thickness.