Electromechanical transfer equations for sandwich-type piezoelectric unit groups

Abstract

The sandwich-type piezoelectric unit group (PUG) constitutes a functional component in piezoelectric transducers, whose dynamic characteristics can be designed and optimized by model-based analysis. However, the conventional transfer matrix method (TMM) faces limitations in modeling a bending-vibration PUG. Specifically, it fails to account for the polarization isolation and the electrode, and lacks the electromechanical transfer conditions for internal elements in the PUG. To overcome these challenges, this paper proposes the electromechanical transfer equation of the sandwich-type PUG. First, the TMM model, characterizing the polarization isolation with dielectric properties, is developed for the piezoelectric ceramic plate (PZT). Then, the electrodes subjected to vibration are retained. The electromechanical transfer conditions are established for the PZT-electrode-PZT situation and the piezoelectric unit (PU)-electrode-PU situation. Subsequently, the bending-vibration transfer equation of the sandwich-type PUG is formulated by combining the bending-vibration PZT model and the electromechanical transfer conditions. Finally, a sandwich-type piezoelectric transducer is employed as a verification case. Numerical results demonstrate that the proposed TMM and finite element method show high consistency in four dimensions: amplitude-frequency characteristics, impedance characteristics, displacement mode shapes, and strain mode shapes. Except for the parallel resonant frequency, all other indicators calculated by the TMM and measured experimentally are in good agreement. This paper proposes a comprehensive modeling methodology for the bending-vibration PUG, facilitating their structural design and optimization. © 2026 Elsevier Ltd