中文摘要：

小尺度封闭空间内部声场的数值计算是声学设计、噪声控制等领域的关键技术。由于波动声学及几何声学方法计算频率上的限制,中频段声场计算问题一直是个难点。本文以声学无网格法为基础,提出了一种基于声粒子分布积分的无网格声场数值计算方法。文中利用声线跟踪理论计算声场中的声粒子分布,并以某个时间点上的声粒子作为蒙特卡罗法中的积分点,将其应用于无网格法中,从而获得声场中的节点声压。利用该方法对一个矩形封闭空间的中低频声场进行了计算,并与模态叠加法、商用声场计算软件、经典无网格法的结果进行了对比,证明基于声粒子分布积分的无网格声场数值计算方法在中低频段相较于传统基于网格的方法具有更高的精度。

英文摘要：

The numerical calculation of the sound fields in small enclosures is an key technique in the areas of acoustical design, noise control, etc. The calculation in the middle-frequency band is a difficult problem because of the frequency limit of the wave-acoustic methods and geometric-acoustic methods. In order to solve this problem, a hybrid method with combinations of the typical meshless method and the particle-distribution integration is proposed in this paper. The particles in the sound field are traced according to the ray-tracing method. Then, the particles at certain time are recorded and considered as the integration points in the Monte Carlo method which is applied in the hybrid method. Finally, the frequency response functions in the middle and low frequency bands of a rectangular enclosure are calculated using the method derived in this paper. The results are compared with those of the modal superposition method, the commercial software, and the classical meshless method. The comparisons show that the method derived in this paper has better accuracy in the middle and low frequency bands than the traditional methods.