Acoustic Eigenvalue Analysis Using Dual Reciprocity Boundary Element Method

The noise control of closed three-dimension domain (such as the cabin, cab, workroom, etc) is practical significance. Modal analysis of an acoustic system can determine its natural frequency and show the distribution of the acoustic quantities in space, give the knowledge about the way that the acoustic system responses are affected when changes are made in the excitation sources or in the domain geometry, and provide valuable information for the noise control of closed three-dimension domain. Because the matrices themselves of the equation which be formed by application of Dual Reciprocity Boundary Element Method (DRBEM) and be used to solve the acoustic field mode, do not implicitly contain the frequency parameter in them, the acoustic eigenvalue problem can be cast into a generalized eigensystem directly and be solved efficiently. This thesis is concerned with the problem of modal analysis of acoustic field using DRBEM.The application of DRBEM to Poisson equation is discussed. A numerical example of two-dimensional problem is given to test the reliability of the DRBEM and the validity of scheme of compiling program, the effect of approximation function and internal node on the numerical results is discussed by compared with exact analytical solutions. The numerical example shows that increasing the item of radial basis function is not a right way to improve the accuracy of results, and more approximation functions should be employed in the DRBEM.DRBEM requires inversion of a matrix formed by approximation function, which makes this method inefficient for large problem. Then the scheme forming for acoustic eigenvalue analysis using non-inversion method is presented. The modal analysis problem of a two-dimensional rectangular acoustic field is solved under two sorts of boundary condition using both inversion method and non-inversion method, and the results are compared with exact analytical solutionsmethod, and the results are compared with exact analytical solutions and that obtained by commercial finite element analysis software ANSYS. The presented example problem clearly demonstrate the validity of the inversion DRBEM, and the non-inversion method is reliable in calculation of acoustic eigenfrequency, yet the resulting eigenvectors can not be used to represent the distribution of acoustic quantities.The approximation functions have crucial effects on the accuracy of DRBEM, and different approximation functions have different performance in varied problems. Therefore selection of the approximation functions is especially important in the eigenvalue analysis of three-dimensional acoustics. A wide range of functions are investigated in solving the eigenfrequency of a 3-D acoustic model under two sorts of boundary conditions. The numerical results show that the performance of these functions on the same discretization and internal nodes and their sensitivity to quantity of internal node is different. The performance of selected functions is discussed and the guideline fot choosingthe approximation functions in acoustic eigenvalue analysis using DRBEM are presented.