加周期纵肋圆柱壳声辐射

Acoustic radiation from an infinite cylindrical shell with internal periodic lengthwise ribs

本文研究了水中加周期纵肋圆柱壳在点力激励下的声辐射特性。壳体振动采用薄壳理论的Donnell方程描述,纵肋振动采用相互独立的梁的纵振动和弯曲振动方程描述。通过周向模态展开和轴向Fourier变换导出圆柱壳体径向振速表达式,使用波数域稳相法积分得到了远场辐射声压的解析解。数值计算给出了接收点正对激励点情况下的远场辐射声压级,并据此进行了机理分析。在加周期纵肋无限长圆柱壳中存在两类辐射机理:亚音速的弯曲波辐射和超音速的Bloch弯曲波分量辐射。由于圆柱壳体表面存在曲率,亚音速的弯曲波也能辐射极小部分能量到远场,并形成频带极窄的共振峰。加周期纵肋圆柱壳在周向是一种无限周期结构,存在多阶次的Bloch弯曲波。低于水中声波数的Bloch弯曲波分量能够通过相位匹配的方式高效辐射到远场。Bloch弯曲波的辐射存在一定的频率下限,其下限与纵肋的间距有关,纵肋间距越大辐射的频率下限就越低。

The acoustic radiation from an infinite cylindrical shell with internal periodic lengthwise ribs was studied in this paper.The motions of the shell were described by the Donnell equations.The lengthwise rib was modeled as an elastic beam,whose motions were decomposed into longitudinal and flexural vibrations.The analytical expressions of the shell motions were obtained through the methods of circumferential mode ex⁃pansion in circumferential and Fourier transform in longitudinal direction.The far-field radiation pressure was gained by applying the stationary phase approach.The acoustic radiation pressure level was calculated by assuming that the observation point was in the far-field and faced the source.The calculation results show that there are two radiation mechanisms for an infinite cylindrical shell with internal periodic lengthwise ribs:(1)the subsonic flexural wave can radiate a small amount of energy to the far-field due to the curvature of the shell;(2)when the cylindrical shell is loaded with periodic lengthwise ribs,multi-order flexural Bloch waves exist in circumferential direction.The supersonic components of the flexural Bloch waves will radiate effi⁃ciently and lead to acoustic radiation resonances in the far-field.