中文摘要：

对纵扭模态叠加型超声振子进行了理论研究，该超声振子由纵扭同频夹心换能器与法兰连接段组成。首先，基于等效电路法和传输线理论，研究了纵向及扭转振动在纵扭同频夹心换能器中的传播规律，得到了该换能器的纵、扭共振的等效电路和频率方程组，并通过合理选择各圆柱段的长度，实现了纵扭同频共振。之后，基于环槽结构具有纵振耦合和扭振隔离的特性，对该换能器进行了简并设计，在其末端构造出了纵、扭简并节点，解决了法兰设置问题。最后，应用有限元软件ANSYS对简并后的超声振子进行仿真分析，结果表明超声振子纵扭共振的同频偏差率得到显著降低。

英文摘要：

The modal superposition type longitudinal-torsional composite ultrasonic vibrator is studied. The ultrasonic vibrator consists of a sandwiched co-frequency longitudinal-torsional transducer and a flange connecting section. First of all, based on equivalent circuit method and transmission line theory, the propagation characteristics of the longitudinal and torsional vibrations in the ultrasonic transducer were analyzed, and the equivalent circuit and longitudinal-torsional resonance frequency equations were derived. Meanwhile, the simultaneous resonance of the longitudinal and torsional vibrations in the sandwich transducer was realized by controlling the cylindrical section length. Then, the longitudinal-torsional degenerate node is constructed on the ultrasonic transducer, by using the characteristics of the ring groove structure with longitudinal vibration coupling and torsional vibration isolation. So, the problem of flange arrangement was solved. At last, the structural dynamic simulation analysis of the new ultrasonic vibrator were carried by the finite element software ANSYS. The results show that the frequency deviation rate of the longitudinal-torsional resonance system is significantly reduced.