On the forced response of waveguides using the wave and finite element method
On the forced response of waveguides using the wave and finite element method
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DOI：
10.1016/j.jsv.2010.07.009
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发表时间：
2010-12
影响因子：
4.7
通讯作者：
J. Renno;B. Mace
中科院分区：
文献类型：
--
作者：
J. Renno;B. Mace
研究了波导在时间谐波载荷作用下的强迫响应。该方法从波和有限元（WFE）方法开始，其中波导的一段使用传统的有限元方法建模。利用截面的质量矩阵和刚度矩阵来构造特征值问题，该问题的解可得到波导的波特性。WFE公式用于计算波导对共轭谐波压力（CHP）的响应。由于对一般激励响应的傅里叶变换是对CHPs响应的线性组合，因此可以通过傅里叶反变换过程获得对一般激励的响应。利用轮廓积分和剩余定理对其进行了分析。因此，本文提出的方法可以通过：(a)使用有限元方法对波导的一段进行建模并对其进行后处理以获得波特性，(b)使用傅里叶变换和轮廓积分来获得波幅值，(c)使用波幅值来找到波导中任何一点的响应。给出了数值算例。
The forced response of waveguides subjected to time harmonic loading is treated. The approach starts with the wave and finite element (WFE) method where a segment of the waveguide is modeled using traditional finite element methods. The mass and stiffness matrices of the segment are used to formulate an eigenvalue problem whose solution yields the wave properties of the waveguide. The WFE formulation is used to obtain the response of the waveguide to a convected harmonic pressure (CHP). Since the Fourier transform of the response to a general excitation is a linear combination of the responses to CHPs, the response to a general excitation can be obtained via an inverse Fourier transform process. This is evaluated analytically using contour integration and the residue theorem. Hence, the approach presented herein enables the response of a waveguide to general loading to be found by: (a) modeling a segment of the waveguide using finite element methods and post-processing it to obtain the wave characteristics, (b) using Fourier transform and contour integration to obtain the wave amplitudes and (c) using the wave amplitudes to find the response at any point in the waveguide. Numerical examples are presented.