Underlying the solution of the modal analysis problem by the BEM is a method for solving a non-linear eigenvalue problem. The method that is derived through frequency interpolation of the matrix described in Section 6.3 is a flexible and consistent method for the modal analysis of the interior Helmholtz problem. However, it may be possible to develop more efficient methods than the QZ algorithm for solving the eigenvalue problem (6.12).
The subroutines described in this Section are flexible in that the wavenumber range over which the resonant frequencies are sought and the number of interpolation points within that range are parameters. In general the sequence of resonant frequencies can be obtained by stepping through the full wavenumber range covering a fixed subinterval at each stage. Ideally users need to determine the wavenumber interval and the number of interpolation points used in each interval to obtain satisfactory solutions with minimum processing time. It is beneficial for users to gain some experience with the methods before using them in practical situations.
The results from the test problems show that the boundary
element method can be confidently applied to the modal analysis
problem. The comparison of
numerical and experimental results
in the application of the methods to the loudspeaker
enclosure show that the BEM is able to extract the
resonant frequencies and mode shapes of an enclosure in a practical
application. The mode shapes shown in the
figures are comparable with those obtained by the
finite element method, see Kirkup and Jones .
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