AI 中文总结
本文提出基于格林函数的通用声学共振态展开（RSE）形式化方法，以二维声学谐振器为例推导微扰矩阵元，其结果与解析解及有限元模拟吻合良好，为声学超材料等领域的共振态方法奠定基础。
AI 中文摘要
共振态展开（RSE）是一种用于开放谐振系统微扰分析的强大模态框架，可直接获取复本征频率与本征模式。尽管RSE在电磁学中已发展成熟，但声学领域的系统表述仍不够完善。本文提出一种基于格林函数的通用声学RSE形式化方法，并以一类二维声学谐振器为例进行说明。采用可解析求解的圆柱参考系统的共振态作为基，推导了密度与压缩率的均匀、径向及扇形变化对应的显式微扰矩阵元，分别对应均匀调谐、渐变轮廓及对称性诱导的模式耦合。将所得复本征频率与本征模式与精确解析解及有限元模拟结果对比，显示出优异的定量一致性。该框架为分析受扰开放声学谐振器提供了系统且物理意义清晰的方法，为声学超材料与非厄米声学中的共振态方法奠定了基础。
英文摘要
Resonant-state expansion (RSE) is a powerful modal framework for the perturbative analysis of open resonant systems, providing direct access to complex eigenfrequencies and eigenmodes. While RSE is well developed in electromagnetism, a comparably systematic formulation for acoustics remains less established. Here, we develop a general Green-function-based formalism for acoustic RSE and illustrate it for a class of two-dimensional acoustic resonators. Using the resonant states of an analytically solvable cylindrical reference system as a basis, we derive explicit perturbation matrix elements for uniform, radial, and sectoral variations of density and compressibility, representing homogeneous tuning, graded profiles, and symmetry-induced modal coupling. The resulting complex eigenfrequencies and eigenmodes are validated against exact analytical solutions and finite-element simulations, showing excellent quantitative agreement. The framework provides a systematic and physically transparent approach for analyzing perturbed open acoustic resonators and establishes a basis for resonant-state methods in acoustic metamaterials and non-Hermitian acoustics.
Comments12 pages, 5 figures, Supplemental Material
