利用边界元法计算无界声场中结构体声辐射

建立了无界声场中结构体声辐射的边界元数学模型 .计算中以八节点曲边四边形等参元模拟结构体表面 .利用复合亥姆霍兹积分方程解决了边界元方法在计算声学外问题时解的不唯一现象 .同时利用正则化关系式将复合亥姆霍兹积分方程中的超奇异数值积分转化为弱奇异数值积分 .最后以脉动球和振荡球声辐射为例 ,验证了数值计算结果 ,表明利用边界元方法计算声学外问题时必须考虑解的不唯一问题

Calculating Acoustic Radiation from Object in Unbounded Sound Field Using Boundary Element Method

A mathematical model about acoustic radiation from structure submerged in unbounded sound field was developed using boundary element method. Eight noded curvilinear quadrilateral isoparametric elements were applied to model the surface of the structure. The nonuniqueness problem occurring in boundary element method when solving the acoustic exterior problems was eliminated using the composite Helmholtz integral formulations. At the same time, the hypersingular numerical integration in the composite Helmholtz integral formulations was converted into weakly singular numerical integration using a regularization relationship. To validate the mathematical model, pulsating sphere radiation and oscillating sphere radiation were calculated. As a result, the numerical results agree very well with the corresponding analytical solutions. In conclusion, the nonuniqueness problem must be considered, when boundary element method is used to solve acoustic exterior problems.