Applications of the Green functions in the study of acoustic problems in open and closed spaces

This paper presents a set of analytical solutions (Green functions) for the steady state response of a homogenous acoustic three-dimensional space sub jected to a point harmonic load or a spatially sinusoidal harmonic line loa d. The propagation medium is modelled with plane surfaces placed so as to r eproduce spaces that vary from a simple half-space to a rectangular paralle lepiped closed space. The final expressions are implemented to evaluate fir st 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 li ne source. The use of these Green functions allows the required BEM discret ization to be limited to the surface of the barrier, avoiding the discretiz ation of the tall building and ground. The calculations are performed in th e frequency domain and time signatures are obtained by means of inverse Fou rier transforms. Complex frequencies are used to attenuate the response at the end of the time frame, which is taken into account by resealing the tim e response. (C) 2001 Academic Press.