求解声学问题的元胞自动机方法

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (16) : 69-74.

论文

求解声学问题的元胞自动机方法

罗锟1，汪振国2

作者信息 +

A cellular automata method for acoustic problems

LUO Kun1，WANG Zhenguo2

Author information +

文章历史 +

摘要

为探究元胞自动机(cellular automata，CA)方法在求解声学问题中的适用性，结合CA原理与声波方程导出一维平面波场CA的局部演化规则，构建出一维声学CA模型，并计算不同边界条件下声管内的声压分布，同时对比解析解验证模型的正确性；以球坐标下的声波方程为基础，推导出脉动球源Y函数的CA局部演化规则，进而建立二维声学CA模型；利用该模型探讨脉动球源声辐射规律，并将分析结果与解析解进行对比。结果表明：所建立的声学CA模型能准确模拟平面波场与球面波场声辐射规律，且结果与解析解吻合程度高；该CA模型可避免传统CA模型中元胞状态各向异性更新的问题；对于双球源组合声场，该CA模型依旧具有良好的适用性。

Abstract

In order to explore the applicability of the cellular automata (CA) method in solving acoustic problems, in this paper, the local evolution rules of one-dimensional plane wave field CA were derived by combining the principle of CA and the acoustic wave equation.On this basis, a one-dimensional acoustic CA model is constructed, and the sound pressure distribution in the acoustic tube under different boundary conditions is calculated.At the same time, the correctness of the model is verified by comparing analytic solution; then, based on the acoustic wave equation in the spherical coordinates, the CA local evolution rule of Y-function of pulsating sphere source is derived, and then a two-dimensional acoustic CA model is established.Finally, the acoustic radiation law of the pulsating sphere source is discussed by using the model, and the analysis results are compared with the analytic solution.The results show that the acoustic CA model can accurately simulate the acoustic radiation rules of plane wave fields and spherical wave fields, and the simulation results are in good agreement with the analytic solution; the CA model in this paper can avoid the problem of anisotropic renewal of a cell state in the traditional CA model, and still has good applicability for the combined sound field of double spherical sources.

导出引用

罗锟，汪振国. 求解声学问题的元胞自动机方法[J]. 振动与冲击, 2021, 40(16): 69-74

LUO Kun，WANG Zhenguo. A cellular automata method for acoustic problems[J]. Journal of Vibration and Shock, 2021, 40(16): 69-74

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