Transmission loss of lined Helmholtz resonator with annular air gap: A Green's function based approach

Abstract

The present article discusses a Green's function-based semi-analytical method to predict the transmission loss of a lined Helmholtz resonator with annular air gap. In the analysis, the walls of the chamber are assumed to be acoustically rigid except at the neck portion where it is treated as a piston source moving with uniform velocity. The Green's function is developed as the summation of eigenfunctions of the central duct. The cumulative effect of the lined portion and the annular air gap including the perforated screens is incorporated as the reflection coefficient in the eigenfunctions. By using the Kirchhoff-Helmholtz integral equation, the velocity potential generated by the piston inside the chamber is evaluated. A transfer matrix relating the acoustic pressure and volume velocity across the neck in the main duct is formulated. The effect of the neck length is included as an added inertance to the impedance in the transfer matrix. The results obtained from the proposed method are validated with the developed numerical models and the experimental data available in the literature. A parametric study has been conducted to investigate the effect of porosity of the perforated screens, thickness and flow resistivity of the absorptive material on the transmission loss of the chamber.