圆板轴对称弯曲振动的模态声辐射效率

Modal Radiation Efficiency of the Axisymmetric Flexural Vibration Circular Plate

采用将声强对辐射面积分的方法获得轴对称弯曲振动圆板在固定、简支及自由边界条件下的模态辐射声功率,进而获得其模态声辐射效率。采用高斯-勒让德数值积分法计算出固定、简支及自由边界条件下圆板的模态声辐射效率的数值解,并将同阶模态三种不同边界条件下的圆板声辐射效率进行了对比。结果表明(:1)圆板的模态声辐射效率在全频段内大体呈现随着振动频率的增高而增大的特点(;2)低频时,圆板的各阶模态声辐射效率接近于零,并且模态阶数越高,低频段模态声辐射效率接近于零的频段范围越宽(;3)对于不同阶模态及三种不同边界条件的圆板,当媒质中的声波波数大于等于板中的弯曲波波数时,板的模态声辐射效率趋近于1(;4)对于固定及简支圆板,中频段内n=1模态的声辐射效率远大于其它模态,而对于自由边界圆板,情况正好相反(;5)对于同阶模态,边界固定时圆板的声辐射效率最高,边界简支时的声辐射效率次之,边界自由时的声辐射效率最低。

The modal radiation efficiency of axisymmetric flexural vibration of circular plates with clamped,simply supported or free boundary condition is discussed by integrating the sound intensity over the surface of the plates.The numerical results are obtained by employing 10 nodes Gauss-Legender integration method.The modal radiation efficiencies with the same mode order but different boundary conditions of the plates are compared.The results show that（1）the modal radiation efficiency increases with the increasing of the frequency in the whole frequency range;（2）the modal radiation efficiency of the plate in low frequency range approaches zero,and the frequency range corresponding to the nearly-zero radiation efficiency becomes wider with the increasing of the mode order;（3）when the sound wave number of the medium is much greater than the flexural wave number of the plate,the radiation efficiency of various modes of the plate with various boundary conditions approaches 1;（4）for edge-clamped plate and simply supported plate,the radiation efficiency of the first order mode is much greater than those of the other modes,while the case is just the reverse for the free-edged plate;and（5）for modes with the same order,the radiation efficiency of the plate with clamped-edge is maximal,that of the simply supported plate takes the second place,and that of the free-edged plate is the minimum.