FEM Investigation of a Multi-neck Helmholtz Resonator

An increasingly significant area of research with several applications in numerous disciplines is that of multi-neck Helmholtz resonators. This study set to explore the accuracy and applicability of finite element method (FEM) for the calculation of the resonance frequency of multi-neck Helmholtz resonators.

FEM is employed for the calculation of the resonance frequency in various cases of multi-neck Helmholtz resonators: with cylindrical or spherical bodies, with unflanged or flanged necks of various dimensions and with various combinations of the above. Also single neck resonators are examined.

FEM results are compared with the results of a recently proposed theoretical model available in the literature and with the outcome of the lumped element approximation (multi-neck) accounting for the added neck surface area. Comparisons revealed little deviation between FEM and theoretical model (less than 1.1% error of calculation for every case). On the contrary in comparison with the lumped element approximation (multi-neck) the error of calculation is significant (up to 40.3% for the cases examined).

FEM will prove useful in expanding our understanding of how multi-neck Helmholtz resonators perform under various conditions and configurations. The present research, which highlights the applicability of FEM for the calculations of the resonance frequency of multi-neck Helmholtz resonators, goes a step further, as the method can be applied in special cases in which it is not trivial to apply an analytical formula. The method can be used for applications of multi-neck Helmholtz resonators for various fields such as acoustic metamaterials, musical acoustics and noise mitigation.