A substructure FMBEM approach is developed for multi-domain sound field computations.The basic approach and process as well as advantages and disadvantages are introduced.Transmission loss of expansion chamber with extended inlet tube is calculated by using substructure FMBEM and conventional boundary element method(CBEM).Availability and accuracy of the approach are validated with experimental result.It indicates that,compared to the CBEM,substructure FMBEM reduces computational time and computational complexity obviously as the number of nodes is increased.

A substructure method and a dual reciprocity boundary element method(DRBEM) are applied to calculate four-pole parameters and transmission loss of ducts and silencers with complex flow.Basic principle and numerical procedure are introduced in detail.It is shown that the DRBEM is valid to compute four-pole parameters and transmission loss of ducts and silencers with subsonic complex flow with higher Mach number.The substructure method reduces numerical complexity of the DRBEM and improves accuracy and computation speed.

The governing equation of three-dimensional sound propagation in an uniform duct with mean flow and linear temperataure gradient is derived,based on the foundamental equations of aerodynamics.By using the interation method,the sound propagation equation is expressed as the case which can be computed numerically with the boundary element method.The four-pole parametes of a muffler can be obtained using BEM,therefore the acoustic per.formance such as transmission loss can be predicted.The transmission loss of an expansion chamber has been calculated and compared with the result obtained by means of the one-dimensional theory.

Bu using the perturbation method, the sound wave propagation equation in the medium with a linear temperature gradient is simplified into Helmholtz equation, which can be computed numerically with the boundary element method. The four-pole parameters of muffler can be obtained using BEM, therefore the acoustic characteristics such as transmission loss can be predicted. The four-pole parameters of a straight duct and transmission loss of an expansion chamber have been calculated and compared with the results obtained by means of one-dimensional theory.

The boundary element method is applied to analyse three-dimensional acoustic characteristics of ducts and expansion chambers with mean flow, The boundary integral equation and fundamental solution of wave propagation in the presence of mean flow have been obtaind. The nine nodes quadratic isoparametric elements areused to discretize boundary surface. The polar coordinate transformation method and indirect method are jointly used to treat singular integration problem, the different partical vibrating velocities are supposed at points of corner, the four-pole parameters of a stright duct and transmission loss of an expansion chamber with and without mean flow have been calculated and compared with results obtained by means of one-dimentional theory and other methods.