Vibration mode coupling in thin-walled cylindrical piezoelectric resonators: Aspect ratio and temperature dependence

Coupled vibration analysis of cylindrical piezoelectric transducers has attracted significant attention over the past decades. Building upon the coupled vibration theory, the phenomenon of mode repulsion between coupled axial and circumferential modes, and the inverse relationship between coupling strength and frequency difference, this work develops a formulation to evaluate the coupling strength in a thin cylindrical piezoelectric shell with an arbitrary aspect ratio. The coupled vibration characteristics of thin-walled cylindrical resonators are systematically investigated as the examples of lead zirconate titanate (PZT-4) ceramics and [001] c-poled Mn-doped 0.24Pb(In _1/2Nb _1/2)O₃-0.46Pb(Mg _1/3Nb _2/3)O₃-0.30PbTiO₃ (PIN-PMN-PT:Mn) single crystals, while clarifying the dependence of vibration mode coupling on geometry and temperature. The results indicate that the temperature-dependent evolution of the maximum coupling strength index follows a trend analogous to that of the coupling coefficient. At fixed temperatures, the coupling strength reaches its maximum value at the mode dividing point (MDP) corresponding to the critical aspect ratio. The comparative analysis demonstrates that the PIN-PMN-PT:Mn resonator exhibits a greater thermal sensitivity relative to the PZT-4 counterpart. In addition, axially poled resonators provide stronger coupling than radially poled configurations. This study provides significant insights into the design of high-precision electromechanical devices utilizing cylindrical piezoelectric resonators.