In this paper, the steady-state and transient sound fields inside 3D enclosed spaces were examined theoretically using the modal expansion method. An analytic formula for the Green’s function was derived allowing to predict the interior sound field for both the harmonic and impulse boundary excitations. A theoretical model was tested numerically for a 3D car-like cavity with a sound absorbing material placed on walls. For a harmonic excitation, calculation results revealed high impact of a frequency and a sound damping on a distribution of the steady-state pressure amplitude. They also indicated irregularly located energy vortices in the active intensity vector field. Simulations of a transient sound field were carried out for a boundary excitation producing a sine wave pulse. Temporal changes in this field were studied using the pressure amplitude determined via the discrete Hilbert transform. A large temporal variability of a distribution of this amplitude was noted due to a strong dependence of a transient sound on a position of the observation point. Simulation results also shown that for a small sound damping on cavity walls, there was an intense sound reverberation inside the cavity.

在本文中，使用模态展开法从理论上研究了3D封闭空间内的稳态和瞬态声场。推导了格林函数的解析公式，可以预测谐波和脉冲边界激励的内部声场。对3D汽车状腔体（在墙上放置了吸音材料）进行了理论模型的数值测试。对于谐波激励，计算结果表明，频率和声音阻尼对稳态压力振幅的分布影响很大。他们还指出了活动强度矢量场中能量涡旋的位置不规则。对产生正弦波脉冲的边界激励进行了瞬态声场的仿真。使用通过离散希尔伯特变换确定的压力幅度研究了该领域的时间变化。由于瞬态声音对观察点位置的强烈依赖性，注意到该幅度的分布具有较大的时间变化性。仿真结果还表明，对于空腔壁上的小声音阻尼，空腔内部存在强烈的声音混响。