This study comprehensively investigates the design principles and performance optimization methodologies for piezoelectric transducers within ultrasonic vibration systems. A primary focus is achieving precise modeling and analysis of Langevin-type piezoelectric transducers. The research team developed an advanced three-dimensional vibration model to recognize the limitations of traditional one-dimensional vibration theory, particularly in analyzing complex vibration coupling phenomena within the transducer structure. This novel model employs the apparent elasticity method for a detailed multidimensional analysis of the critical longitudinal-radial coupling vibration characteristics. Mechanical coupling coefficients were systematically incorporated as fundamental parameters throughout the design process. To establish a robust numerical analysis framework, SOLIDWORKS for three-dimensional geometric modeling was seamlessly integrated with COMSOL Multiphysics for multiphysics finite element numerical. This integrated approach facilitated effective vibration modeling, comprehensive numerical analysis of the transducer design. Consequently, the methodology successfully revealed essential transducer characteristics, including nodal plane position 71 mm, resonance frequency 19.393 kHz, head displacement amplitude 36.1 μm and complex vibration mode shapes.