Applications of the Green Functions in the Study of Acoustic Problems in Open and Closed Spaces.

Abstract

This paper presents a set of analytical solutions (Green functions) for the steady state response of a homogenous acoustic three-dimensional space subjected to a point harmonic load or a spatially sinusoidal harmonic line load. The propagation medium is modelled with plane surfaces placed so as to reproduce spaces that vary from a simple half-space to a rectangular parallelepiped closed space. The final expressions are implemented to evaluate first the pressure field inside a rectangular parallelepiped room, whose walls allow different absorption coefficients. Then, the acoustic scattering of a three-dimensional sound source by an infinitely long rigid barrier in the vicinity of a tall building is evaluated using the boundary-element method (BEM), making use of the analytical solution for a spatially sinusoidal line source. The use of these Green functions allows the required BEM discretization to be limited to the surface of the barrier, avoiding the discretization of the tall building and ground. The calculations are performed in the frequency domain and time signatures are obtained by means of inverse Fourier transforms. Complex frequencies are used to attenuate the response at the end of the time frame, which is taken into account by rescaling the time response.