Analysis of Factors Determining the Helmholtz Resonator Eigenfrequency

In this paper the Helmholtz resonator geometry influence on its eigenfrequency is investigated using acoustic calculations. To perform acoustic calculations the finite element method was used. First of all, ANSYS software was used to create a resonator geometry model using finite elements of a certain size and shape. Thus, we used non-uniform partitioning of the model into finite elements. A more detailed partitioning was done in the vicinity of the resonator neck. Then, the resulting configuration was imported in SYSNOISE program to perform acoustic calculations. The calculation results allowed us to determine resonator eigenfrequency and identify dependences of the eigenfrequency on the geometric features of the resonator and of the duct in which it is located.The work considers the concentric Helmholtz resonators in ducts of circular and square cross-sections, when the neck of the resonator is a hole in the wall of the duct. Then for a duct of square cross-section two Helmholtz resonator models with its different location are considered. In the first model the resonator is located on the sidewall of the duct, and the second resonator is concentric. For a concentric resonator also the relationship between the attached length of the neck resonator and the chamber diameter was studied. Carried out researches have allowed us to establish that the shape of the resonator camera has a smaller effect on the eigenfrequency of the resonator than the geometry of its neck. The main parameter that defines the eigenfrequency of Helmholtz resonators with the same geometrical parameters is the attached length of the neck resonator. In turn, the attached length of the neck resonator is determined, mainly, by the ratio of neck diameter to the diameter of the duct. The obtained results allow us to improve the accuracy of estimating the eigenfrequency of Helmholtz resonators thereby giving an opportunity to improve the quality of their acoustic design.</p