中文摘要：

阶梯形变幅杆具有易于加工、变幅比大的优点，是常用的四种单一变幅杆之一。有限元方法是一种成熟、可靠的数值模拟方法。建立了阶梯形变幅杆的有限元模型，用有限元方法研究了一组阶梯形变幅杆的谐振频率，比较了阶梯形变幅杆谐振频率的有限元分析结果、理论值和实验值，分析了三种方法在变幅杆设计中的优缺点及各自产生误差的原因。

英文摘要：

Stepped ultrasonic horn is available in a lot of cases because it is easy to machine and provides large amplitude ratio between the two ends of the ultrasonic horn. Finite element method has become a proven and reliable numerical simulation method. A finite element model of the stepped ultrasonic horn is established to study tile effect of cross - section area ratio between the two ends of the ultrasonic horn at the resonance frequency of the stepped ultrasonic horn. The results obtained by the finite element analysis, the analytic computation and the experiment are compared, and it is found that the finite element method is utilizable and produces more precise results than the analytic computation. The advantages and disadvantages of the three methods, and the causes of the discrepancy arc also discussed.