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This paper presents a computational technique using Boundary Element method for the prediction of sound radiated by axisymmetric bodies with arbitrary boundary conditions. By taking the advantage of the axisymmetric property of the body the three dimensional integral formulation is reduced to one dimensional integral along the generator of the body. The arbitrary boundary conditions is expanded in Fourier series with a period of 2π. The integral equation is solved using superposition principle involving each term of the series. By adding the result associated with each term the final solution is obtained. A numerical procedure is implemented using curvilinear isoparametric element representatation. Examples are given involving an oscillating sphere and a half vibrating sphere. The results are compared with the analytical solution in which good agreement has been obtained.

The Boundary Element Method (BEM) is a computational method for solving the acoustic wave equation when the acoustic domain has an irregular or arbitrary shape. The BEM is distinguished from other numerical methods such as the finite element method in that with the BEM only the surface or the boundary of the acoustic domain needs to be discretized. In this paper some examples are presented concerning problems in automotive industry involving the radiation of sound from engines and other vibrating structures, the acoustical response of passenger compartments of vehicles and the attenuation of mufflers and other exhaust or intake system components.

A two-microphone method is presented to measure in-duct acoustic properties such as normal impedance, absorption coefficient and transmission loss by using random signal excitation. By measuring the distance between the microphones and the wave spectra the normal impedance, acoustic absorption coefficient and transmission loss can be determined. Bias and random errors are also discussed to estimate the accuracy and precision of estimates of acoustic properties abtained from the acoustic pressure measurements from the two microphones. The analysis shows that the bias errors can be reduced by using a small analysis bandwidth and by measuring the acoustic pressure close to the non-source end of the duct. The random errors, on the other hand, can be minimized by maintaining a high coherence between the acoustic source and the pressure in the duct. Test cases of the method are shown for close tube, single layer glasswool and double layer glasswool.

An advanced computational method is presented for calculating the sound radiated by vibrating engine of arbitrary shape. The method is based on the numerical evaluation of the Helmholtz Integral Equation. In particular an isoparametric element formulation is introduced in which both the surface geometry and the acoustic variables on the surface of the vibrating body are represented by second order shape functions within the local coordinate system. The formulation includes the case where the surface may have a non-unique normal (e.g. at edges or corners). A general result for the surface and field velocity potential is derived. Test cases involving spherical geometry are given for a pulsating sphere and for an oscillating sphere in which the analytical solutions are known. Examples for bodies with edges and corners are shown for the problems of radiation from a circular cylinder and from a pulsating cube.