中文摘要：

计算了圆柱截面阶梯形变幅杆的一阶到六阶纵振动模式的谐振频率,较系统地分析研究了带与不带过渡段的阶梯杆之谐振频率随其粗细段长度比和直径比的变化规律,得到了一些新结果.用两种方法计算谐振频率：一种是求解一维近似解析频率方程,计算程序用MATLAB编制.另一种是用有限元仿真数值计算,利用ANSYS软件,且适合对于任意材料和几何参数的圆截面阶梯杆的任意阶谐振频率的计算.有限元计算与一维近似理论计算得到的频率的变化趋势基本一致.所给频率变化趋势对于变幅杆的设计和加工都能提供参考.在相当大的阶梯杆几何参数空间内,一阶谐振频率随变幅杆粗段与过渡段长度而相应减小.对于实测频率比所期望值高的变幅杆进行频率调整时可以利用上述性质.

英文摘要：

Longitudinal vibration frequencies of the first to the sixth orders modes of stepped ultrasonic horns, with and without taper-transitional section, were calculated. Computations are performed with MATLAB programming based on the one-dimensional theory, and with ANSYS based on the finite element method （FEM）, respectively. Systematic studies on the natural frequencies of horns are carried out, and some new rules obtained, with variations of the length ratio and section diameter ratio of the horn. Reduction of the length of thick rod or the length of transitional section can lower the first order natural frequencies of the horn, which is useful in adjusting the frequency response of a horn during machining processes.