Reliability analysis of different geometric configurations of Helmholtz resonators for a sustainable performance

A Helmholtz resonator (HR), consisting of a cavity connected to a neck, is widely used for noise control at a specific tuning frequency determined by the neck cross-sectional area and length, cavity volume, and speed of sound. Uncertainty in geometric parameters and air properties can significantly influence the tuning frequency and transmission loss, thereby affecting HR performance. In this study, finite element analysis is employed to optimise the geometry of an HR integrated with a duct system. In addition, a reliability analysis is carried out by considering normally distributed random variables governing HR performance. Six neck–cavity configurations, namely cylinder–cylinder, cuboid–cylinder, cylinder–cuboid, cuboid–cuboid, cylinder–sphere, and cuboid–sphere, are analysed using a six-sigma-based reliability approach. The results indicate that the tuning frequency can deviate by up to 10% from the target value due to uncertainties. Experimental validation using an additively manufactured HR duct system demonstrates similar trends in frequency shift and peak transmission loss within the range of 6–10% from the desired tuning frequency. The findings highlight the importance of reliability-based design to ensure consistent and sustainable HR performance. Helmholtz resonators provide an effective and environmentally friendly passive acoustic solution for industrial noise control and can be extended to other noise-sensitive environments.