矩形薄板的模态声辐射效率

A Thin Rectangular Plate's Modal Radiation Efficiency

将声强对辐射面积分获得四边简支矩形板的模态辐射声功率的精确解析表达式,进而求得其模态辐射效率。采用10节点的高斯-勒让得求积法求得模态辐射效率全频段数值解。结果表明:方形薄板模态阶数越低,其声辐射效率越大;对于同一模态,频率越高,其中低频段的声辐射效率越大;低频时,奇-奇模态的辐射效率远远大于奇-偶模态或偶-偶模态。对于节线所围区域为方形时的矩形薄板,低频时奇-奇模态的辐射效率远远高于奇-偶模态;对于奇-奇模态,模态阶数越低,其辐射效率越大,而对于奇-偶模态则表现恰好相反。高频时,各类各阶模态的声辐射效率相差不大,都近似为1。

The modal radiation sound power is obtained by integrating the sound intensity in the surface of the rectangular plate,thus the expression of the modal radiation efficiency is obtained.The numerical results of the modal radiation efficiency of the rectangular plate with simply supported boundary are obtained in the whole frequency range by 10 nodes Gauss-Legendre integration method.It is found that the lower modes of the square plate with simply supported boundary have greater sound radiation efficiency than the higher ones,and for the same mode,the radiation efficiency will become greater with the increase of the frequency.In the lower frequency range,the radiation efficiency of the odd-odd mode is greater than the odd-even mode and the even-even mode.It is also observed that the odd-odd mode of the rectangular plates with the square intranodal area（the area between adjacent node lines） has greater radiation efficiency in the lower frequency range than the odd-even mode.For the odd-odd mode,the lower the mode is,the greater the radiation efficiency is,while the truth is just the reverse for the odd-even mode.In the higher frequency range,the radiation efficiency of various modes approaches 1.