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Acoustics recently became a versatile platform for discovering novel physicaleffects and concepts at a relatively simple technological level. On this way,single resonators and the structure of their resonant modes play a central roleand define the properties of complex acoustic systems such as acousticmetamaterials, phononic crystals, and topological structures. In this paper, wepresent a powerful method allowing a qualitative analysis of eigenmodes ofresonators in the linear monochromatic acoustic domain based on multipoleclassification of eigenmodes. Using the apparatus of group theory, we explainand predict the structure of the scattered field knowing only the symmetrygroup of the resonator by connecting the multipolar content of incident andscattered fields. Such an approach can be utilized for developing resonatorswith predesigned properties avoiding time-consuming simulations. We haveperformed full multipole symmetry classification for a number of resonatorsgeometries, and tightened it with scattering spectra profiles.

Acoustic resonators: symmetry classification and multipolar content of the eigenmodes