基于复数矢径的波叠加法解声辐射问题

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

利用波叠加法与结构动力分析中的相似性 ,提出了一种在波叠加法中克服解非唯一的通用方法 ,即在虚拟源强系统中加入一定的虚拟阻尼从而能获得全波数域内的唯一解 ,并以此为基础提出了一种新的加入虚拟阻尼的方法———复数矢径波叠加法 .文中给出了脉动球和摆动球两个数值算例 ,计算结果表明 :本文方法不仅能有效解决数值求解过程中解非唯一的问题 ,且计算时间只与标准波叠加法相当 ,计算精度却比同类方法高 .

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format to overcome the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed in this paper. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wavenumbers can be ensured. Based on this thought, a novel method--wave superposition method with complex radius vector is constructed. Not only the computational time of this method is approximately equal to that of the standard wave superposition method, but also the accuracy is much higher comparing with the other correlative methods. At last, taking pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can overcome the non-uniqueness problem effectively.