BOUNDARY ELEMENT METHOD IN CAVITY NOISE PROBLEMS

Abstract

The present study focuses on the application of the Boundary Element Method (BEM) to cavity noise problems governed by the reduced non-homogeneous differential wave equation. The aim is to treat the acoustic effect of internal sound source, absorbent materials pasted on the vibrating surface and to predict the acoustic effect of structural modification and internal sound source modification in a 3- dimensional enclosed domain. Furthermore, predicting a point source strength in a cavity from measurements obtained at several points is also carried out. In chapter 2, mathematical formulation (boundary integration equation-BIE) is established and some relevant theory is presented. Integration of the BIE is performed numerically. Its implementation is divided into five steps. The isoparametric quadratic elements and an effective technique to treat nearly singular integral are described in detail. From chapter 3 to chapter 4, a FORTRAN program, called BEACOU, is introduced. The program is verified by comparing the numerical solution with the analytical solutions available for the acoustic distributions in a long rectangular duct and in a sphere, and against experimental measurements. An experimental setup is designed and assembled for the verification. Numerical results obtained for all examples are found to be in good agreement with the exact analytical solutions and measured results in the interested range of frequency. It is proven that BEACOU package can be used as an effective and accurate tool for acoustic design against cavity noise problems. The pre- and post- processing were carried out by I/FEM, a general purpose finite element analysis software. In chapter 5, the BEACOU package is used to analyze the acoustic percentage of contribution due to boundary vibration. i.e. APC analysis and the acoustic percentage of contribution of interior sound source, i.e., APCSS analysis . The results lead to three conclusions. Firstly, for engineers doing noise control, they can directly specify the regions where structural modification should be made with the APC information obtained with BEACOU. The information is also of value for the placement of active noise control sources on the existing structure to yield the best reduction of sound pressure at point(s) in the cavity. Secondly, any structural modification should be a compromise after a survey over a wide range of frequency, because the APC information strongly depends on the wavelength of the sound. A region may be most sensitive to the interior sound pressures at one particular frequency, but insensitive at other frequencies. Thirdly, the sound source in the cavity can be used as a control source if its characteristic is selected properly. The study shows that the control sound source in the cavity is very effective for noise reduction at low frequencies.