Abstract: A universal defining equation of ultrasonic vibration system is derived, with its definite solution ascertained involving both linear and nonlinear boundary conditions. Then, based on the wave theory, universal defining equation of composite radius-changing horn is given in exponential form, and the linear boundary condition is set to solve the sectionalized nonlinear equation to derive the general expressions of wave node position and amplification coefficient relevant to the horn. Furthermore, the nonlinear boundary condition is set to provide the definite solution to the nonlinear dynamic model of the system. The numerical results reveal that the definite solution gives a correct expression to the dynamic characteristic of ultrasonic vibration system and wave motion of the horn, thus providing theoretically a reference for other ultrasonic vibration system.