基于有限元法的跨介质声传输数值模拟与分析
Numerical Simulation and Analysis of Cross-Media Acoustic Transmission Based on the Finite Element Method
DOI: 10.12677/aam.2026.153088, PDF,    国家自然科学基金支持
作者: 张佳旺：青岛大学数学与统计学院，山东 青岛；赵胜东*：宁波大学极端环境交叉力学研究中心，浙江 宁波
关键词: 有限元法；等效介质模型；水声超表面；低频共振；Finite Element Method； Equivalent Medium Model； Underwater Acoustic Metasurface； Low-Frequency Resonance
摘要: 在由空气、薄冰层与水体构成的跨介质体系中，由于不同介质之间存在显著的声阻抗差异，声波在界面处易发生强烈反射，导致声能透射效率显著降低，从而制约了薄冰环境及实验室理想条件下跨介质声学测试与感知研究的发展。针对这一问题，本文从数学建模与数值分析的角度出发，建立了一种适用于毫米级薄冰条件的跨介质声传输等效介质模型，并在此基础上构建相应的有限元数值计算框架。通过对单元结构进行参数化建模，将其等效为亚波长介质层，从而将复杂的多介质界面声学问题转化为可求解的边值问题。基于有限元方法对该模型进行数值离散与求解，系统分析了单元几何参数及阵列结构对声能传输特性的影响。数值仿真结果表明，在单元共振频率附近，体系中的声能透射效率显著提升，且有限元计算结果与等效介质模型预测具有良好一致性。研究结果验证了所建立的数学模型及有限元数值方法在毫米级薄冰及实验室理想环境条件下分析跨介质低频声传输问题的有效性，为相关声学结构的设计与优化提供了一种可行的数值分析工具。
Abstract: In cross-media systems composed of air, thin ice layers, and water, the pronounced acoustic impedance mismatch among different media leads to strong wave reflection at the interfaces, resulting in a significant reduction in acoustic energy transmission efficiency. This limitation restricts the development of cross-media acoustic testing and sensing research under thin-ice and laboratory ideal conditions. To address this issue, this study approaches the problem from the perspectives of mathematical modeling and numerical analysis. An equivalent medium model applicable to millimeter-scale thin-ice conditions is established to describe cross-media acoustic transmission, and a corresponding finite element numerical framework is developed on this basis. By parameterizing the unit-cell structure and treating it as a subwavelength effective medium layer, the complex acoustic problem involving multiple media interfaces is transformed into a solvable boundary value problem. The resulting model is discretized and solved using the finite element method, and the effects of unit-cell geometric parameters and array configurations on acoustic energy transmission are systematically investigated. Numerical simulation results demonstrate that the acoustic energy transmission efficiency of the system is significantly enhanced in the vicinity of the unit-cell resonance frequency, and that the finite element results show good agreement with the predictions of the equivalent medium model. The results validate the effectiveness of the proposed mathematical model and finite element numerical method in analyzing low-frequency cross-media acoustic transmission under millimeter-scale thin-ice and laboratory ideal conditions, providing a feasible numerical analysis tool for the design and optimization of related acoustic structures.
文章引用：张佳旺, 赵胜东. 基于有限元法的跨介质声传输数值模拟与分析[J]. 应用数学进展, 2026, 15(3): 70-80. https://doi.org/10.12677/aam.2026.153088

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