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The Fourier version of the Variational Theory of Complex Rays for medium-frequency acoustics

机译:中频声学复射线变分理论的傅里叶版本

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The Variational Theory of Complex Rays (VTCR) is a wave-based computational approach dedicated to the resolution of medium-frequency problems. It uses a variational formulation of the problem which enables one to use any type of shape function within the substructures provided that it satisfies the governing equation. Thus, the solution can be approximated using plane waves, which is very interesting in the medium-frequency vibration domain and also leads to a strong convergence of the method. In the previous works, this was shown in the case of acoustic problems in which the amplitudes of the plane waves were calculated as wavebands. In this paper, we propose a new approximation of these amplitudes based on Fourier series. We show that this approach increases the robustness of the method, makes it more efficient numerically and extends its applicability to somewhat higher frequencies.
机译:复射线变分理论(VTCR)是一种基于波的计算方法,致力于解决中频问题。它使用问题的变体形式表示,只要满足控制方程式,就可以在子结构中使用任何类型的形状函数。因此,可以使用平面波来近似求解,这在中频振动域中非常有趣,并且也导致了该方法的强大收敛性。在以前的工作中,这是在声学问题的情况下显示出来的,在声学问题中,平面波的幅度被计算为波段。在本文中,我们提出了基于傅立叶级数的这些幅度的新近似值。我们表明,该方法提高了方法的鲁棒性,使其在数值上更有效,并将其适用性扩展到了更高的频率。

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