不同比率的矩形活塞声源辐射阻抗的研究

Numerical Calculation of Radiation Impedance of the Rectangular Piston in Different Ratios

从辐射阻抗的定义式出发,推导了矩形活塞辐射阻抗的四重积分表达式,借助5个节点的高斯数值积分方法编程,计算了r(长与宽之比)不同时矩形活塞声源辐射阻抗的数值解,并绘制出辐射阻、辐射抗随k(ab^(1/2))和r的变化关系曲线。结果表明,当活塞的形状一定时,其振动频率越高,面积越大,辐射阻及辐射声功率也越大;当振动频率和活塞面积均一定时,活塞形状越接近正方形,其辐射阻及辐射声功率也越大;随着频率及活塞面积的增大,活塞形状越接近正方形,同振质量由峰值下降越迅速。

Quadruple integral expressions of the radiation impedance in rectangular piston are deduced in this paper. The Numerical results of the resistance and reactance in different ratios are calculated with the method of Gaussian numerical integral by 5 nodes. Two curves of radiation resistance and radiation reactance are drawn after calculating the results. It can be seen from the curves that the radiation resistance is the function of k √ab and r, and so is the radiation reactance. When the shape of the piston is certain, the radiation resistance and the sound power are greater with the increasing of the frequency and the area of the piston. When the frequency and the area are certain, the more the shape reaches the square, the greater the radiation resistance and the sound power are. With the increasing of the frequency and the area of the piston, the more the shape reaches,the square, the faster the adnexed mass decreases from the top.