Application of the time domain formulation of the method of equivalent sources to radiation and scattering problems

The time domain formulation of the method of equivalent sources is used to approximate the Green's functions of small volume sources in front of arbitrarily shaped structures. Access to such a set of Green's functions simplifies the radiation problem to a numerical evaluation of a surface integral similar to the Rayleigh integral. Especially for the calculation of the radiated power, this method offers a substantial advantage concerning the computational effort. The concept of equivalent sources is traditionally used in the frequency domain and it represents an attractive alternative to the boundary element method (BEM) for calculating the sound radiation from vibrating structures with arbitrary shapes, mainly because of the lower computational effort required by the method of equivalent sources in comparison with the BEM. The time domain formulation is shown to lead to a further improvement of the method. A faster algorithm and thereby a lower demand for computational power are consequences of changing from the frequency to the time domain. The theoretical formulations for both the time domain formulation and for the approximated Green's functions are presented. With this general formulation the method is usable for sound radiation problems as well as for scattering problems. The function of the method is demonstrated and tested. The sound radiation from a simply supported plate which is excited by a force pulse is calculated. This plate is part of a rectangular box where the other walls are assumed to be rigid. However, the method is not restricted to transient processes, as the Green's function can be convolved with arbitrary source signals.