A simplified boundary element method (BEM) for dealing with high frequency sound is proposed. The boundary integral equation is modified into a quadratic form to enable the prediction of sound levels in the one-third octave band analysis. Monopole and dipole source terms in the conventional BEM are transformed into the auto- and cross-spectra of two vibrating sources, in which the cross-spectra are eventually neglected by assuming that the correlation coefficients involved are negligible.
The present method is compared with the Rayleigh integral for calculating the sound pressure radiated from baffled beam and baffled panel, in terms of the application limit. The characteristic length of the boundary element and the applicable frequency range are determined by the lower limit value of the correlation coefficient. As a test example, the field pressure radiated from a partially vibrating sphere is predicted and the resultant trend is in good agreement with the analytic solution as far as the related correlation coefficient satisfies the assumption. The over-determination process for overcoming the nonuniqueness in exterior problems is found to be unnecessary in the present method because the phase information is ignored. The results of the calculation show that the proposed method is acceptable for solving the exterior radiation problem at high frequency range in a timely manner.
As an application example, the present method is adopted to abruptly calculate the one-third octave band levels radiated from a muffler as an arbitrary shape radiator. The muffler jacket is excited at a point by a shaker and the velocity distribution on the irregular surface is measured by using a laser vibrometer. The predicted result by the present method agrees with the measured pressure level within 3 dB errors. The results show that they are the acoustic field forms a monopole-like radiation pattern at the far-field without nonuniqueness error.
