圆柱壳水中平面振动和声辐射的导纳法研究

On the vibration in a plane perpendicular to the axis and sound radiation of a cylindrical shell in water by mobility method

目的探索水下结构振动声辐射问题的导纳法求解。方法从无限长圆柱壳的振动方程出发，利用流体和圆柱壳分界面上振速连续边界条件，推导出了圆柱壳在母线方向均匀分布的径向线力激励下，平面振动声辐射效率以及辐射声场的模态导纳表达式。数值求解了辐射效率和模态导纳随频率的变化关系以及辐射声场指向性。结果①在n〈5情况下圆柱壳平面振动模态辐射导纳的实部随频率变化明显；当n从5变到50过程中，模态辐射导纳的实部随频率变化出现振荡现象。圆柱壳平面振动模态辐射导纳的虚部为负，且绝对值随／1,增大而增大。②圆柱壳在妒=0处受沿母线方向均匀分布的简谐（f=10-1010Hz）线力激励时，水中辐射声场的指向性（r=10α）介于“∞”型和“∞”和“8”叠加的形状之间。结论导纳方法对于求解水下规则结构声辐射问题是可行的。

Aim To investigate the mobility solution method of the sound radiation from vibrational structures in water. Methods Based on the vibration equation of an infinite circular cylindrical shell and continuous boundary conditions of velocity on the surface of the cylinder shell and water, the expressions of sound radiation efficiency and sound field of the shell by mobility have been derived on the condition that it is excited by a harmonic line ra- dial force uniformly distributing along the generator. The relationships between radiation efficiency and frequency, and between modal mobility and frequency, and the directivity pattern of the sound field are numerically solved. Results ①When n 〈 5, the real part of the modal mobility of the cylindrical shell vibrating in a plane perpendicular to the axis changes obviously with the frequency, and when 5 〈 n 〈 50, it oscillates with the change of the frequency. The imaginative part of the modal mobility of the shell is always less than zero, and the absolute value of it increases with n. ②When the cylinder is excited at φ =0 by a harmonic（f= 10 - 1 010Hz） line radial force uniformly distributing along the generator, the directivity pattern of the sound field （r = 10a） is between ＂∞＂pattern and ＂∞ ＂and ＂8＂ superposeition pattern. Conclusion The mobility solution method is feasible for the sound radiation from regular structures in water.