Simulation of the 3D sound pressure level inside closed absorbing acoustic rooms bounded by non-parallel floor and ceiling surfaces, and parallel sidewalls

摘要

A model for the simulation of three-dimensional (3D) sound pressure level generated by acoustic sources inside closed rooms bounded by non-parallel floor and ceiling surfaces is presented. The 3D problem is solved as a sequence of two-dimensional (2D) problems with different spatial wavenumbers kz, after a spatial Fourier transform has been applied along the z direction, which is the width of the room. The problem uses a boundary element method (BEM) formulation in the frequency domain. The use of analytically appropriate Green's functions for wedges, defined by means of an image model technique, allows the required BEM discretization to be limited to the back and front walls of the room and avoids the discretization of the other flat surfaces. The computations are first performed in the frequency domain and inverse Fourier transforms are subsequently applied to obtain time responses. Complex frequencies are used to avoid the time-aliasing phenomenon. This effect is later taken into account by re-scaling the response in the time domain. The model allows frequency dependent absorption coefficients to be defined for the various walls. In the case of the ceiling, floor and lateral room surfaces the absorption is introduced through the direct manipulation of the analytical Green's functions. The absorption of the back and front walls is simulated using impedance boundary conditions. Once the algorithm has been verified against a 3D BEM model, the potential of the proposed procedures is illustrated by simulating the propagation of waves generated by a point source inside an auditorium.