In order to realize the longitudinal-torsional vibration of the ultrasonic horn in cutting and welding process, the dual incentive longitudinal-torsional compound vibration characters of the composite stepped ultrasonic horn with a circular cone was analyzed, and the resonance frequency equations and the vibration velocity amplification coefficient for the design of longitudinal-torsional composite vibration the horn were derived. At the same time，the simultaneous resonance of the longitudinal and torsional vibrations in the horn was realized by reasonable choosing three section length of composite horn. The structural dynamic characteristics of composite horns were analyzed by the finite element software ANSYS. It is shown that the calculated resonance frequencies of the horns are in good agreement with the simulation results, and the longitudinal vibration and torsional vibration resonance frequency in the horn is almost equal to each other.

longitudinal-torsional compound vibration; co-frequency resonance; composite horn; finite element analysis (FEM)