基于声粒子分布积分的无网格声场计算方法

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。

A meshless method based on the particle-distribution integration for simulations of sound fields in small enclosures

The numerical calculations of the sound fields in small enclosures are important to the acoustical design, noise control, etc. The calculations in the middle frequency band have always been a difficult problem because of the frequency limit of the present commonly used methods. In order to solve this problem, a meshless method based on the particle distribution integration is derived in this paper. At first, the system equation for calculating the sound pressure of nodes is derived according to Galerkin weighted residual method, as well as the method for constructing shape functions. Then, the particles in the sound field are traced according to the ray-tracing method. The particles at some certain time are recorded and considered as the integration points in the Monte Carlo method which is applied in the meshless 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 the results obtained using modal superposition method and commercial software. The comparisons show that the method derived in this paper has higher accuracies in the middle and low frequency bands than the traditional method.