THREE-DIMENSIONAL ACOUSTIC ANALYSIS OF CONCENTRIC TUBE RESONATOR USING GREEN'S FUNCTION

A three-dimensional acoustic model is developed to characterize the performance of a concentric tube resonator by using Green's function. Green's function is expressed in terms of acoustic mode shape of the annular cavity with inner wall impedance conditions. Lumped parameter model has been used for calculating specific acoustic impedance to relate the pressures across the perforated liner portion. The acoustic domain is assumed to be rigid, except at inlet and outlet, which are the locations of piston sources. The total pressure acting on each piston is evaluated by using superposition principle of acoustic pressures developed at both inlet and outlet port locations. The transfer matrix, relating acoustic state variables at upstream and downstream ends is obtained, and transmission loss is calculated to estimate the performance of the configuration. These results have been compared with that of the numerical models developed using Finite Element Methods, and good agreement has been obtained.