求解水中结构声辐射特性的虚拟声源方法研究

Research on virtual sound sources method for calculating sound radiation characteristics of underwater structure

利用模态展开法和波叠加原理,发展求解水中结构声辐射特性的方法,进一步将波叠加原理与有限元法（FEM）相结合,提出求解结构声辐射特性的半虚拟声源半FEM算法.将结构动力学方程中的声压项表示为结构表面振速积分的形式,或者将结构动力学方程和结构与介质交界面相容性条件中的声压项表示为虚拟声源函数的组合形式,对所得方程进行模态展开和傅里叶逆变换,分别建立关于振动模态系数的求解方程和虚拟声源强度与振动模态系数的耦合方程,然后根据波叠加原理,确定虚拟声源强度,获得两种求解结构声辐射特性参数的方法.最后,利用FEM和波叠加原理建立结构的动力学方程,结合交界面相容性条件,获得耦合的求解方程,从而确定虚拟声源强度.以水下矩形板为例进行了辐射声功率求取,并讨论了对虚拟声源数目的敏感性.结果表明：本方法具有较高的计算精度,尤其适用于低频声辐射问题的计算;由耦合方程计算声辐射特性参数时,无须计算结构的辐射阻抗,提高了计算效率.

By using modal expansion method and the principle of wave superposition,a method was developed to calculate the sound radiation characteristics of underwater structures.Furthermore,by combining the principle of wave superposition and the finite element method（FEM）,a semi-virtual sound source and semi-FEM algorithm was proposed to solve the structural acoustic radiation characteristics.By means of expressing the sound pressure of structural dynamic equation as the integral form of the vibration speed on structure surface or taking the sound pressure of structural dynamic equation and compatility conditions at the surface as combinations of virtual sound source function,then dealing with the equation with expanding the vibration modal and inverse Fourier transform,the equation about the coefficient of vibration modal and the coupling equation about vibration modal and sound source intensity could be established.Based on the principle of wave superposition,the sound source can be determined and the two methods could be obtained.Further,by using FEM and the principle of wave superposition,the dynamic equation of the structure was established.The coupled equation was obtained by combining with the compatibility conditions,so as to determine the strength of the virtual sound source.The sound power was calculated with the example of a rectangular plate and its sensitivity to the number of virtual sound sources was discussed.Results shows that proposed method have high precision,which is especially suitable for the problem of low frequency sound radiation; when coupling equation is adopted by the method,computing radiation impedance is unnecessary,so calculating efficiency is improved.