FEM Investigation of a Multi-Neck Helmholtz Resonator

Abstract

An increasingly significant area of research with several applications in numerous disciplines is that of multi-neck Helmholtz resonators. This research is set to explore the accuracy and applicability of the finite element method (FEM) for the calculation of the resonance frequency of multi-neck Helmholtz resonators. The FEM is employed for the estimation 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. The 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 the 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). The 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 the FEM for the calculations of the resonance frequency of multi-neck Helmholtz resonators, goes a step further; this approach can be applied in special cases where 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.

FEM Investigation of the Air Resonance in a Cretan Lyra

“…Collectively, the results of the air frequency for measurements and modeling are presented in Table 1. The distribution of the acoustic pressure and the sound pressure levels for the air resonances (Figures 6 and 8) is typical in the case of the 'air resonances' of musical instruments [43,44] or the Helmholtz resonance for typical resonators [45,46]. For example, the acoustic pressure and the sound pressure levels have the lowest values in the sound holes of the lyra (similar to the values in the neck of the resonators).…”

Tunable Helmholtz Resonators Using Multiple Necks

“…The same can be observed when there is a leak or a gap in the body of the resonator [40,41]; therefore, the understanding of the phenomenon is important for predicting the acoustic behavior of the resonator. For the numerical investigation of multi-neck Helmholtz resonators, various methods have been applied such as the boundary element method (BEM) [40] and finite element method (FEM) [42,43]. Among computational methods, FEM is probably the most widely used in the field of noise control [44], in architectural and environmental acoustics [45][46][47][48] and also in the frequency and the time domain [49][50][51].…”