Prediction of transmission loss in mufflers by the finite−element method

A numerical technique based on the finite−element method has been developed for analyzing the performance of systems of acoustic elements including expansion chambers in mufflers. The theories developed are, firstly, the variational formulation of the acoustic field existing in the system and, secondly, the finite−element approximate solutions of the variational problems. The predictions of transmission loss are then made by forming the equivalent acoustic four−terminal transmission network in which the acoustic four−pole constants are calculated from the finite−element method. As used, the finite−element approach is perfectly general and may be applied to any system component with arbitrary boundary geometry provided this may be realized by an assembly of rectangular elements. The method is applied to simple expansion chamber models because the results are tractable and theoretical results from acoustic filter theory are available for comparison purposes. The comparison brings out an important fact: the accuracy of the prediction of transmission loss implies that the variational formulation and finite−element approximations are adequately applicable to a number of practical applications. Subject Classification: 50.40; 20.40.