近水面有限长谐振动圆柱的远场声学模型研究

Far-filed acoustic Model analysis of a finite harmonic vibrating cylinder near the free surface

摘要:

本文提出了求解近水面有限长谐振动圆柱远场声学特性的解析方法。首先，基于镜像原理，以假定的虚源考虑自由液面影响；再结合Graf加法定理，将虚、实源各声压项进行合并，转换到波数域后，得到声压的简洁显示表达式；最后，重要指标—远场辐射声压则可利用稳相法进行求取。根据所需研究的声学成分，提出了对应的数学物理模型，有利于深入研究自由液面和结构表面互散射机理。研究结果表明，自由液面的影响可归纳总结为类偶极子效应，且该效应对辐射声与散射声计算结果均有显著影响，但二者除相似传播规律外还存在不可忽视的相位差；散射声压随次数增大将以固定倍率衰减，且衰减速率与圆柱壳的浸没深度成正比，但与壳体表面谐振动激励频率成反比。

Abstract:

An analytical method is proposed to study the far-field acoustic characteristics of a finite harmonic vibrating cylinder close to the free surface. Firstly, based on the Image method, the influence of free liquid level is taken into account with a hypothetical virtual source. Then, combined with the Graf’s addition theorem, the sound pressure items of virtual and real sources are combined and converted into wavenumber domain to obtain a simple expression of sound pressure. Finally, the important index, the far-field radiated sound pressure, can be obtained by the Stationary phase method. Two kinds of mathematical physical models are established to deeply research the mechanism of acoustic scattering between the free surface and the structural surface. The results show that the influence of free liquid level can be summarized as the acoustic dipole, which has significant influence on the calculated results of radiated and scattered sound, but there are phase differences that can not be ignored except for similar propagation laws. The scattered sound pressure decreases at a fixed rate with increasing number of times, and the attenuation rate is proportional to the submergence depth of the cylindrical shell, but inversely proportional to the excitation frequency of the resonance vibration on the shell surface.