بازنگری معادله ساوربری: دریافت هایی از مدلسازی چندپدیده ای میکروترازوی کریستال کوارتز به روش المان محدود

The quartz crystal microbalance (QCM) is a versatile surface-acoustic-wave-based gravimetric sensor widely used in biosensing, vapor and gas detection, thin film monitoring, corrosion studies, polymer adsorption, and surface interaction analysis. In this work, a comprehensive finite element method (FEM) simulation framework for QCM crystals is presented using COMSOL Multiphysics. The model couples solid mechanics, piezoelectricity, and electrostatics to predict resonance behaviour with high accuracy. Validation against analytical calculations showed close agreement, confirming the reliability of the approach. The study further examines the influence of crystal radius on the resonance frequency constant, providing insights into the applicability of the Sauerbrey equation. Results confirm that the Sauerbrey relation underestimates resonance frequency at low diameter-to-thickness ratios because of the edge effect and has relatively low accuracy, while at higher ratios the simulated and analytical values agree within 2.64%. Overall, the proposed FEM framework deepens understanding of QCM behaviour and supports the development of more accurate and efficient sensor designs.