弯曲振动矩形板辐射阻抗的计算

本文推导了四边简支矩形板的辐射阻抗表达式, 利用高斯数值积分方法, 计算了其相对辐射阻抗的数值解. 由不同模态下相对辐射阻抗与频率以及不同长宽比对应的相对辐射阻抗与频率的关系可知, 在中低频段, 模态越低, 辐射阻抗越大, 也就意味着辐射声功率和同振质量越大; 对于一定面积和模态的矩形板, r (r=a/b, 长与宽之比)值越接近1, 即越接近正方形, 辐射阻和辐射抗越大. 本文的方法能对其他复杂边界条件下的、无振动解析解的矩形板的辐射阻抗数值量级大小提供一个参考, 也可由计算弯曲振动的阻抗自然地过渡到活塞振动阻抗的计算.

Calculations of radiation impedance of a rectangular plate with flexural vibration

The radiation impedance expressions of flexural vibration rectangular plate with simply supported boundary are derived, and the numerical results are obtained by using the Gauss numerical integral method. Some conclusions can be obtained on the basis of the curves of relative radiation impedances versus frequency in the different modes and those corresponding to different aspect ratios. The lower the mode, the greater the radiation impedance in the low frequency is, so are the acoustic radiated power and the quality with vibration. For a rectangular plate of certain area and mode, the more the value of r (r = a/b, aspect ratio) approximates to 1, that is, the closer the square is, the greater the radiation resistance and the radiation reactance are. The method offers a reference for determining magnitude of the radiation impedance of the rectangular plate in other complicated boundary conditions (they may be no analytical displacement solutions). The method of calculating the radiation impedance of flexural vibration can be naturally transplanted into the case of piston vibration.