圆形超声辐射器的多维耦合振动

用解析方法研究了圆形超声辐射器的多维耦合振动，通过引入振动轴向振动与横向振动之间的机械耦合系数，导出了辐射器耦合振动共振频率方程的解析表达式，由此不仅能够得出振子的轴向共振频率，而且可以得出震子的径向共振频率，与一维理论的结果相比，本文得出的结果与实测值更加符合，实验表明，振子共振频率的测量值与计算值符合很好。

Multi dimensional Coupled Vibration of Circular Ultrasonic Radiator

The multi dimensional coupled vibration of circular ultrasonic radiator is studied by using the analytical method. By introducing mechanical coupling coefficients between axial and transverse vibrations of the vibrating body and ignoring shear stresses, the analytical expressions of resonance frequency equations on coupled vibration of the radiator are obtained. Different from one dimensional theory, the coupled vibration has two kinds of resonance frequency, i.e., axial and radial, and the latter is deduced by applying these expressions. So it is evident that all the vibrations of any vibrator are multi moded and have multiple resonance frequencies, though they can be considered approximately as a single mode in some peculiar cases. Compared with the numerical method, this method presented has the advantage of simple calculation and explicit physical meaning. Some test data and one dimensional results are employed to verify the validity of the method presented. And by comparison, it is evident that these calculated values obtained after the multidimensional theory of resonance frequency of a vibrator are in good agreement with the measured data, and are more accurate than those of one dimensional theory.