In this work, a new kind of shape horn is studied.Based on the theory of fixedaxis rotation of rigid body , the torsional vibration equation of variable crosssection is established. By optimizing the inverse proportion function , the analytical solution of ultrasonic horn is obtained. According to the boundary conditions, the various parameters of ultrasonic horn, such as the magnification, resonance length, and the input impedance are derived. Finally, the model of ultrasonic horn′s torsional vibration is simulated by using the finite element software ANSYS , the results of resonance frequency modal are consistent with that of the theoretical value.

Inverse proportion function born; torsional vibration ;magnification; equivalent circuit; finite element modal analysis