粗细端等长阶梯形变幅杆的有限元分析

本文利用有限元分析软件ANSYS研究了一组粗细端截面积比不同的阶梯形变幅杆，得出了每个变幅杆的第一阶和第三阶谐振频率、粗细端分界面的相对位移和振幅放大系数。结果表明：ANSYS仿真值与实测值的平均偏差仅为0．3％，远小于常用式解析值与实测值的偏差；变幅杆粗细端分界面的运动类似受牵引的薄膜运动；而振幅放大系数与面积比成正比的结论可扩展到粗细端截面积比为100的情况。

Finite element analysis of stepped ultrasonic transformer with equal-length sections

Finite element method (FEM) is used, through software ANSYS, to analyze stepped ultrasonic transformers, the two sections of which have the same length but different cross-sectional areas. The resonance frequency, the displacement pattern of the interface between the two sections, and the amplitude amplifications of the first-and the third-order vibration modes are computed for each transformer. The results show that the average deviation (0.3%) between the ANSYS simulated frequencies and the experimentally measured values is much less than that between the frequencies calculated from the conventional formula and the experimental; the movement of the section interface of the transformer is similar to that of a towed membrane; a linear relationship between the amplitude amplification and the cross-section-area ratio is obtained, which applies to the later ratio as high as 100.