仿生平面三角形单元积分声场的波函数构造
Construction of Wave Function for Integrating Sound Field with Biomimetic Planar Triangular Elements
贺佐潦霜 1陆泽琦 2丁虎 3陈立群2
作者信息
- 1. 上海大学 微电子学院,上海 201800;上海大学 力学与工程科学学院,上海 200444
- 2. 上海大学 微电子学院,上海 201800;上海大学 力学与工程科学学院,上海 200444;上海市应用数学和力学研究所,上海 200072;上海市能源工程力学重点实验室,上海 200072
- 3. 上海大学 力学与工程科学学院,上海 200444;上海市应用数学和力学研究所,上海 200072;上海市能源工程力学重点实验室,上海 200072
- 折叠
摘要
波叠加法在求解声源外部辐射声场时,需要对所有离散单元进行数值积分计算导致计算效率较低,而等效源法由于过度简化单元始终存在较大的积分近似误差.针对以上缺陷,利用Helmholtz方程在球坐标系下的解构造了一种与单元积分等效且无需积分的波函数.受仿生复合材料三角形缝合结构启发,以适用范围最广的平面三角形单元为例,构造了波函数的一般形式和内推形式.最后,通过数值仿真对比了两种波函数与直接积分的计算声场的精度和效率.结果表明,两种波函数与直接积分的计算误差低于0.5％,且内推波函数的计算效率约为直接积分的6倍.
Abstract
The wave superposition method requires numerical integration of all discrete elements when solving the external radiation sound field of the sound source, resulting in low computational efficiency. However, the equivalent source method always has significant integration approximation errors due to excessively simplifying the elements. In response to the above shortcomings, a wave function that is e-quivalent to element integration and does not require integration was constructed using the Helmholtz e-quation in a spherical coordinate system. Inspired by the triangular stitching structure of biomimetic composite materials, taking the most widely applicable planar triangular element as an example, the general and internal forms of the wave function were constructed. Finally, the accuracy and efficiency of the two wave functions and the direct integration calculation of the sound field were compared through numerical simulation. The results show that the calculation error between the two wave functions and direct integration is less than 0.5％, and the calculation efficiency of the extrapolated wave function is a-bout 6 times that of direct integration.
关键词
波函数/平面三角形单元/单元积分/波叠加法/等效源法Key words
wave function/planar triangular element/element integration/wave superposition method/equivalent source method引用本文复制引用
基金项目
国家自然科学基金(12272210)
国家自然科学基金(11872037)
国家自然科学基金(11872159)
出版年
2024
NETL
NSTL
万方数据