“…At present, although most analytical and semi-analytical solutions have been proved to be correct near the resonance frequency, many mechanical properties have been ignored due to the simplification of the model. The finite element technique is a powerful numerical tool which has been proved to be able to simulate the thickness shear vibration of quartz crystal microbalances well [ 24 , 25 , 26 , 27 , 28 , 29 ]. The finite element equation of structural mechanics and electrostatic coupling of AT cut quartz crystal element is as follows [ 30 ]: where , and are the mass, damping and stiffness matrices of structure, respectively.…”