A two-dimensional approach for sound attenuation of multi-chamber perforated resonator and its optimal design

A two-dimensional (2D) method is investigated to predict the acoustic performances of single-chamber perforated reactive resonators. The effect of non-planar wave propagation on the acoustic performance of acoustically short and long resonator is studied. A desirable resonance behavior appears in acoustically short chamber substantially below the cut-off frequency due to non-planar wave propagation. Adding inlet/outlet extensions has similar effects to that of reducing perforation rate on acoustic performances for short-length perforated resonators. Based on the 2D approach, a 2D transfer matrix method (TMM) is developed through solving the acoustical continuity functions under two outlet boundary conditions to predict the acoustic performances of multi-chamber perforated resonators (MCPRs) which can attenuate broadband noise. Comparisons between the calculations and tests show that the 2D TMM is much more accurate than one-dimensional approach within entire frequency range. In order to evaluate its engineering applicability, a new optimization procedure including a targeted transmission loss curve and a reasonable objective function is introduced to optimize the structure parameters of a MCPR with three chambers using a genetic algorithm. The result can meet the target well at desired frequencies under space constraint. The theoretical method developed in this work can be used for the calculation and optimization of MCPRs in various applications.