伸缩虚边界元法解含任意形状空穴外场声辐射

An expanding-contracting virtual boundary element method for solving the vibration and sound radiation from a cavity with an arbitrary shape

以位势理论为基础 ,提出了求解含任意形状空穴外场声辐射的伸缩虚拟边界元法 .该方法的核心是通过伸缩虚拟边界使相应内问题的特征频率 (本征值 )避开与外问题给定波数相重合 ,从而保证了解的唯一性 .以二维情况为例 ,通过诸多不同空穴形状在谐激励作用下的声辐射算例 ,从计算精度、稳定性以及克服解的非唯一性等方面 ,对该方法进行了检验 .计算结果表明 :无论是远场或近场的辐射声压 ,该方法都具有非常高的效率和精度 .

Based on the potential theory, an expanding contracting virtual boundary element method (ECVBEM) is presented to solve the vibration and sound radiation from a cavity with an arbitrary shape. The main advantage of the method consists in keeping the eigenfrequency of the corresponding interior problem away from the given wave number of the original Helmholtz exterior problem, ensuring the uniqueness of the solution obtained. Tests of the ECVBEM are carried out on its calculating accuracy and stability as well as the ability to overcome the non uniqueness of solution through examples of two dimensional Helmholtz exterior problems. The calculation results of the different shapes of cavities under harmonic excitation show that the sound pressures in the far and near field obtained by the present method are highly accurate and efficient.