Determination of Transmission Loss in Slightly Distorted Circular Mufflers Using a Regular Perturbation Method

Abstract

A perturbation-based approach is implemented to study the sound attenuation in distorted cylindrical mufflers with various inlet/outlet orientations. Study of the transmission loss (TL) in mufflers requires solution of the Helmholtz equation. Exact solutions are available only for a limited class of problems where the method of separation of variables can be applied across the cross section of the muffler (e.g., circular, rectangular, elliptic sections). In many practical situations, departures from the regular geometry occur. The present work is aimed at formulating a general procedure for determining the TL in mufflers with small perturbations on the boundary. Distortions in the geometry have been approximated by Fourier series expansion, thereby, allowing for asymmetric perturbations. Using the method of strained parameters, eigensolutions for a distorted muffler are expressed as a series summation of eigensolutions of the unperturbed cylinder having similar dimensions. The resulting eigenvectors, being orthogonal up to the order of truncation, are used to define a Green's function for the Helmholtz equation in the perturbed domain. Assuming that inlet and outlet ports of the muffler are uniform-velocity piston sources, the Green's function is implemented to obtain the velocity potential inside the muffler cavity. The pressure field inside the muffler is obtained from the velocity potential by using conservation of linear momentum. Transmission loss in the muffler is derived from the averaged pressure field. In order to illustrate the method, TL of an elliptical muffler with different inlet/outlet orientations is considered. Comparisons between the perturbation results and the exact solutions show excellent agreement for moderate (0.4∼0.6) eccentricities.