Ek. Skarsoulis, 2ND-ORDER FOURIER SYNTHESIS OF BROAD-BAND ACOUSTIC-SIGNALS USING NORMAL-MODES, Journal of computational acoustics, 5(4), 1997, pp. 355-370
A scheme for approximate normal-mode calculation of broadband acoustic
signals in the time domain is proposed based on a second-order Taylor
expansion of eigenvalues and eigenfunctions with respect to frequency
. For the case of a Gaussian impulse source a closed-form expression i
s derived for the pressure in the time domain. Using perturbation theo
ry, analytical expressions are obtained for the involved first and sec
ond frequency-derivatives of eigenvalues,and eigenfunctions. The propo
sed approximation significantly accelerates arrival-pattern calculatio
ns, since the eigenvalues, the eigenfunctions and their frequency-deri
vatives need to be calculated at a single frequency, the central frequ
ency of the source. Furthermore, it offers a satisfactory degree of ac
curacy for the lower and intermediate order modes. This is due to the
fact that essential wave-theoretic mechanisms such as dispersion and f
requency dependence of mode amplitudes are contained in the representa
tion up to a sufficient order. Numerical results demonstrate the effic
iency of the method.