幂函数超声变幅杆理论研究与模态分析

依据变截面杆纵向振动波动方程，给出了幂函数形变幅杆的频率方程及重要参数计算公式，并与其他类型变幅杆进行比较．结果表明，幂函数变幅杆具有与指数形变幅杆相同的放大系数，与阶梯形变幅杆有相同的谐振长度，且这种变幅杆不存在截止频率．用有限元软件Ansys进行模态分析表明，幂函数形变幅杆共振频率的模态分析值与一维理论值吻合．

Theoretical study and modal analysis of an power function horn

Based on the wave equation of longitudinal vibration of variable cross-section rod, the frequency equation and some important parameter formulas of an power function horn are deduced. Compared with other type of ultrasonic horns, the results show the amplitude factor of power function horn is the same as that of the exponential type and the resonance length is equal to that of stepped type. Meanwhile, it is discovered that this kind of ultrasonic horn has no cut-off frequency. Finally, the modal analysis is obtained and the resonance frequency is determined by using finite element software Ansys. It is shown that the simulation result is consistent with that of the theory.