Thickness-Mode Nonlinear Vibration of Quartz Crystal with Initial Stress and Cut-Identification for Optimal Frequency Sensitivity

Quartz crystals are widely used in sensors, auctors, filters, and resonators due to their excellent piezoelectric properties and operational stability. As electronic devices continue to miniaturize, understanding the nonlinearity in quartz crystal structures becomes increasingly important. This study aims to support the design of high-sensitivity piezoelectric sensors by analyzing the thickness-mode nonlinear vibration of randomly cut quartz crystals, incorporating the effects of initial stress. Specifically, a theoretical framework is developed to determine the nonlinear vibration frequencies of the fast and slow thickness-shear modes, as well as the thickness-stretch mode in a randomly cut quartz crystal. The study explores the dependence of vibration frequencies on nonlinear vibration amplitude and initial stress. To ensure that frequency variations are attributed to initial stress, the nonlinear vibration amplitude is maintained at a reasonable value. Furthermore, the effects of cut orientation on frequency variation under a given initial stress are examined to identify the optimal cut for frequency sensitivity. Our results demonstrate that quartz crystals exhibit high sensitivity to initial stress, with the fundamental vibration mode showing the largest frequency shift despite having the lowest frequency. This mode proves particularly suitable for sensor applications. The study identifies the cut orientation with the optimal frequency sensitivity and provides insights that could guide the design of piezoelectric sensors and expand their application.