Resonance analysis of a high temperature piezoelectric disc for sensitivity characterization

Ultrasonic transducers for high temperature (200 °C+) applications are a key enabling technology for advanced nuclear power systems and in a range of chemical and petro-chemical industries. Design, fabrication and optimization of such transducers using piezoelectric materials remains a challenge. In this work, experimental data-based analysis is performed to investigate the fundamental causal factors for the resonance characteristics of a piezoelectric disc at elevated temperatures. The effect of all ten temperature-dependent piezoelectric constants (ε₃₃, ε₁₁, d₃₃, d₃₁, d₁₅, s₁₁, s₁₂, s₁₃, s₃₃, s₄₄) is studied numerically on both the radial and thickness mode resonances of a piezoelectric disc. A sensitivity index is defined to quantify the effect of each of the temperature-dependent coefficients on the resonance modes of the modified lead zirconium titanate disc. The temperature dependence of s₃₃ showed highest sensitivity towards the thickness resonance mode followed by ε₃₃, s₁₁, s₁₃, s₁₂, d₃₁, d₃₃, s₄₄, ε₁₁, and d₁₅ in the decreasing order of the sensitivity index. For radial resonance modes, the temperature dependence of ε₃₃ showed highest sensitivity index followed by s₁₁, s₁₂ and d₃₁ coefficient. This numerical study demonstrates that the magnitude of d₃₃ is not the sole factor that affects the resonance characteristics of the piezoelectric disc at high temperatures. It appears that there exists a complex interplay between various temperature dependent piezoelectric coefficients that causes reduction in the thickness mode resonance frequencies which is found to be agreement in with the experimental data at an elevated temperature.