A two-dimensional model on the coupling thickness-shear vibrations of a quartz crystal resonator loaded by an array spherical-cap viscoelastic material units

•Use a two-dimensional model instead of the one-dimensional transmission line model.•Influence of loadings on admittance of a compound QCR system has been involved in.•The results of our model are consistent with the existing experiment data.

We establish a two-dimensional model on the coupling thickness-shear mode (TSM) vibrations of a quartz crystal resonator (QCR) carrying an array of spherical-cap (SC) viscoelastic material units. The electrical admittance of the compound QCR system is described directly in terms of the physical properties of the surface material units. The admittance spectra about the tendon stem cells (TSCs) acquired from our calculation are compared with the existing experiment data and found to be consistent with each other, indicating our model has good veracity and reliability in analyzing the mechanical properties of covered loadings. Furthermore, we calculate admittance spectra of surface Epoxy Resin (SU-8) units with different geometrical configurations and bulk effect. It is found that both geometrical configuration and bulk effect produce influence on the resonant frequency and admittance of the compound QCR system.