This thesis deals with the implementation of the dual reciprocity boundary element method for problems governed by the Helmholtz equation. The main emphasis is the simulation of acoustic cavities, such as passenger compartments of aeroplanes and of cars. The boundary element method is a numerical analysis scheme which only needs a discretisation of the boundary of the domain of interest. The dual reciprocity boundary element method is a variation of this technique. The advantage of applying this special scheme for the Helmholtz equation is that in the final equation, unlike with the 'classical' boundary element method, the matrices are independent of the wave number. The Helmholtz problems in this research involve different geometries, properties and dimensions. A total of seven codes are employed, ranging from one- to three-dimensional problem solvers. The one-dimensional code is capable of solving related eigenfrequency and wave generation problems. Three of the two-dimensional codes are applied to eigenfrequency analysis: one is based on the constant element, one uses linear elements and one employs quadratic elements. A final two-dimensional code is used for wave propagation problems and uses the constant element. The three-dimensional codes are applied to eigenfrequency analysis only; one uses constant triangular elements, and another employs linear triangular elements. The kernel integrations in the two- and three-dimensional codes are all based on analytical solutions, given in this thesis. A new method of quadratic element kernel integration is described in detail. The three-dimensional triangular boundary element kernel integrations are based on improved analytical formulations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:639309 |
| Date | January 1994 |
| Creators | Verhoeven, N. A. |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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