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.