矩形薄板超声辐射器弯曲振动模式及本征频率研究

Study on natural vibration and resonance frequency of rectangular radiators in flexural vibration

对不同边界条件下矩形薄板的弯曲振动进行了分析 ,得出 3种边界条件下(自由、简支、固定 )矩形薄板的本征频率方程 ,并对其振动模式进行了研究 .理论分析表明 ,经典的细棒弯曲振动理论以及矩形薄板的条纹振动模式 ,是弯曲振动矩形薄板的一些极限振动模式 .实验表明 ,弯曲振动矩形薄板的共振频率测试值与计算值符合很好 ,且矩形薄板弯曲振动位移分布的理论与实测结果一致 .

The flexural vibration of rectangular thin plate radiators is studied. The resonance frequency equation and the displacement distribution are derived when the boundary conditions are free, simply supported and clamped, respectively. Theoretical analyses show that the traditional flexural vibration of a slender rod and the stripe vibration mode of a rectangular thin plate are the limiting vibration modes of rectangular plates in flexural vibration, the results can be derived directly from the theory of this paper. It is shown that the measured resonance frequencies are in good agreement with the calculated results, and the flexural displacement distribution is also consistent with the theoretically predicted results.