Abstract: In order to solve the problem of the design of the ultrasonic atomizing nozzle’s vibration system composed of certain elements of thin rod without simple analytic solutions, a piecewise approximate simulation method is proposed, and based on the method, an ultrasonic atomizing nozzle’s vibration system is designed. Using mechanic-electric analogy method, based on the four terminal network of the common longitudinal vibration of thin rod with variable cross-section, the thin rod without simple analytic solutions is divided into many parts to simulate the whole rod, then the overall transmission matrix of the vibration system is built up, and as a result, the design and analysis of the vibration system is achieved. Using different simulation accuracy values, calculates three kinds of half wavelength solid and hollow single horns with the shape like exponent, cone and catenary are calculated, then the simulation calculation results and the theoretical results are compared and analyzed. At the same time, three kinds of half wavelength solid and hollow compound horns with the shape like exponent- cylinder, cone-cylinder and catenary-cylinder are calculated and the simulation calculation results and the theoretical results are compared and analyzed. Compared with the simulation results and the theoretical value, it can conclude that simulation results are very close to the theoretical calculation value and piecewise approximation simulation calculation method can solve the problem of the thin rod’s longitudinal vibration’ design which variable cross section without simple analytic solutions. Based on the four terminal network transmission matrixes piecewise approximate simulation method, the nozzle’s vibration system is designed and analyzed，and the manufactured nozzle can work well.

Key words: Four terminal network, Piecewise approximate, Transmission matrix, Ultrasonic nozzle