基于声线法的特殊体育馆模型中声场均匀性分析

Study of sound field uniformity in 3D stadium model by ray-tracing algorithm

采用声线法得到体育馆模型和三维矩形空间中声线传播特性,通过Wolf方法计算了体育馆模型和矩形空间的李雅普诺夫(Lyapunov)指数,得到两个空间声线系统的混沌特性。通过比较两个空间中声线传播的位置和方向遍历特性,探索几何空间形状对声场均匀性的作用。研究表明,这类特殊体育馆模型是一个有两个正的Lyapunov指数的超混沌结构。声线在体育馆模型空间的传播有着位置和方向的遍历性,而在矩形空间中只有位置的遍历性,没有方向的遍历性。通过声学软件Odeon对体育馆模型和三维矩形空间进行仿真,采用彩色网格计算多个维度平面位置的声压级差异并做整体对比。可以看到,空间几何形状对声场均匀性有着重要的作用。

In this paper,a method of mapping ray motions in three-dimensional(3D)enclosed space is proposed,and a ray-tracing algorithm is used to describe the paths of ray propagation in a rectangular space or 3D stadium model.The ray chaotic characteristic is discussed by using Wolf method to calculate the largest Lyapunov exponents(LLEs)of the ray systems in the rectangular space and the 3D stadium model.By comparing the ergodicity of position and direction in the two spaces,the effect of geometry on sound field uniformity is explored.The study shows that the 3D stadium model is a hyper-chaotic structure with two positive Lyapunov exponents(LE),in which the ray has the ergodic characteristics of position and direction,whereas the rectangular room is a regular one,in which the ray only has the ergodic characteristics of the position rather than the direction.The acoustic uniformity is evaluated by the difference of the sound pressure levels(SPLs)at different positions in the sound field by using Odeon room acoustics software.The results show that the geometry has significant effect on acoustic field uniformity.