3-D acoustic analysis of spherical chamber having single inlet and multiple outlet

Abstract

The Transmission Loss (TL) performance of spherical chambers having single inlet and multiple outlet is obtained analytically through modal expansion of acoustic field inside the spherical cavity in terms of the spherical Bessel functions and Legendre polynomials. The uniform piston driven model based upon the impedance [Z] matrix is used to characterize the multi-port spherical chamber. It is shown analytically that the [Z] parameters are independent of the azimuthal angle (φ ) due to the axisymmetric shape of the sphere; rather, they depend only upon the polar angle (θ ) and radius of the chamber R₀. Thus, the effects of relative polar angular location of the ports and number of outlet ports are investigated. The analytical results are shown to be in good agreement with the 3-D FEA results, thereby validating the procedure suggested in this work.