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A three-dimensional acoustics model using the method of fundamental solutions

机译：使用基本解法的三维声学模型

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摘要

The method of fundamental solutions (MFS) is formulated in the frequency domain to model the sound wave propagation in three-dimensional (3D) enclosed acoustic spaces. In this model the solution is obtained by approximation, using a linear combination of fundamental solutions for the 3D Helmholtz equation. Those solutions relate to a set of virtual sources placed over a surface placed outside the domain in order to avoid singularities. The materials coating the enclosed space surfaces can be assumed to be sound absorbent. This effect is introduced in the model by imposing impedance boundary conditions, with the impedance being defined as a function of the absorption coefficient. To impose these boundary conditions, a set of collocation points (observation points) needs to be selected along the boundary. Time domain responses are obtained by applying an inverse Fourier transform to the former frequency domain results. In order to avoid "aliasing" phenomena in the time domain results, the computations introduce damping in the imaginary part of the frequency. This effect is later removed in the time domain by rescaling the response. After corroborating the present solution against the analytical solution, known in closed form for the case of a parallelepiped room bounded by rigid walls, the model is used to solve the case of a dome.
机译：在频域中制定了基本解法（MFS），以模拟声波在三维（3D）封闭声空间中的传播。在此模型中，使用3D亥姆霍兹方程的基本解的线性组合通过近似获得解。这些解决方案涉及一组虚拟源，这些虚拟源放置在放置在域外部的表面上，以避免奇异。可以认为覆盖封闭空间表面的材料是吸声材料。通过强加阻抗边界条件将这种效应引入模型中，其中将阻抗定义为吸收系数的函数。为了施加这些边界条件，需要沿着边界选择一组并置点（观察点）。时域响应是通过对先前的频域结果应用傅立叶逆变换获得的。为了避免在时域结果中出现“混叠”现象，计算在频率的虚部引入了阻尼。稍后，通过重新缩放响应，可以在时域中消除此影响。在将本解决方案与分析解决方案进行核对后，对于以刚性墙为边界的平行六面体房间而言，该解决方案以封闭形式公知，然后使用该模型解决圆顶问题。

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