The impedance matrix method is applied to study the scattering of flexuralwaves propagating in an infinite thin plate containing an $N$-beam resonator.The resonator consists of a circular hole containing a smaller plate connectedto the background plate by a number $N$ of rectangular beams. Afterrepresenting the boundary conditions in a modal multipole expansion form, acompact expression is obtained for the T-matrix, which relates the incident andthe scattered transverse (out-of-plane) waves. The analysis of the scatteringcross-section reveals interesting scattering features, like resonances andanisotropy, associated with this type of resonators. Numerical experimentsperformed within the framework of the finite element method support theaccuracy of the model here developed.
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机译：阻抗矩阵法用于研究在包含$ N $光束谐振器的无限薄板中传播的弯曲波的散射，该谐振器由一个圆孔组成，该圆孔包含一个较小的板，该板与背景板相连，矩形的个数为$ N $梁。在以模态多极展开形式表示边界条件之后，获得了T矩阵的紧凑表达式，该表达式将入射波与散射的横向（面外）波联系起来。散射截面的分析显示了与这种类型的谐振器相关的有趣的散射特征，例如谐振和各向异性。在有限元方法框架内进行的数值实验支持此处开发的模型的准确性。
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