Abstract
In this study, a coupling dynamic model on an acoustic wave sensor system, consisting of a thickness-shear mode quartz crystal resonator (QCR) and an array of surface nanowires (NWs), has been established including the surface effects of NWs. The governing equations of NWs are derived from the Timoshenko beam theory in consideration of shear deformation and rotary inertia. The electrical admittance is described directly in terms of the physical properties of the surface NWs from an electrically forced vibration analysis. The effects of residual surface tension \(\tau _{0}\) and surface elasticity \(E_\mathrm{s}\) of NWs on the admittance spectra and vibration modes of the compound QCR system are examined, and some useful results are obtained, which will be helpful to the design of nanosized beams loaded acoustic wave sensors and some related applications.
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References
Benes, E.: Improved quartz crystal microbalance technique. J. Appl. Phys. 56, 608–626 (1984)
Li, F., Wang, J.H.-C., Wang, Q.-M.: Thickness shear mode acoustic wave sensors for characterizing the viscoelastic properties of cell monolayer. Sens. Actuators B Chem. 128, 399–406 (2008)
Qin, L., Cheng, H., Li, J.M., Wang, Q.-M.: Characterization of polymer nanocomposite films using quartz thickness shear mode (TSM) acoustic wave sensor. Sens. Actuators A Phys. 136, 111–117 (2007)
Reed, C.E., Kanazawa, K.K., Kaufman, J.H.: Physical description of a viscoelastically loaded AT-cut quartz resonator. J. Appl. Phys. 68, 1993–2001 (1990)
Liu, B., Jiang, Q., Yang, J.: Frequency shifts in a quartz plate piezoelectric resonator in contact with a viscous fluid under a separated electrode. Int. J. Appl. Electromagn. Mech. 35, 177–187 (2011)
Liu, N., Yang, J., Wang, J.: Shear vibration of a crystal plate carrying an array of microbeams. Philos. Mag. Lett. 91, 572–581 (2011)
Kong, L., Xie, X., Zhang, J., Wang, Y., Hu, Y.: On the interaction between a quartz crystal resonator and an array of micro-beams in thickness-shear vibrations. Acta Mech. Solida Sin. 28, 464–470 (2015)
Kong, L.-C., Hu, Y.-T.: Effect of strain-gradients of surface micro-beams on frequency-shift of a quartz crystal resonator under thickness-shear vibrations. Acta Mech. Sin. 31, 647–652 (2015)
Xie, J., Hu, Y.: A two-dimensional model on the coupling thickness-shear vibrations of a quartz crystal resonator loaded by an array spherical-cap viscoelastic material units. Ultrasonics 71, 194–198 (2016)
Xie, J., Hu, Y.: Electric admittance analysis of quartz crystal resonator in thickness-shear mode induced by array of surface viscoelastic micro-beams. Appl. Math. Mech. 38, 29–38 (2017)
Husain, A., Hone, J., Postma, H.W.C., Huang, X.M.H., Drake, T., Barbic, M., Scherer, A., Roukes, M.L.: Nanowire-based very-high-frequency electromechanical resonator. Appl. Phys. Lett. 83, 1240–1242 (2003)
Li, M., Mayer, T.S., Sioss, J.A., Keating, C.D., Bhiladvala, R.B.: Template-grown metal nanowires as resonators: performance and characterization of dissipative and elastic properties. Nano Lett. 7, 3281–3284 (2007)
Chen, C.Q., Shi, Y., Zhang, Y.S., Zhu, J., Yan, Y.J.: Size dependence of Young’s modulus in ZnO nanowires. Phys. Rev. Lett. 96, 1–4 (2006)
Jing, G.Y., Duan, H.L., Sun, X.M., Zhang, Z.S., Xu, J., Li, Y.D., Wang, J.X., Yu, D.P.: Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy. Phys. Rev. B Condens. Matter Mater. Phys. 73, 1–6 (2006)
Lachut, M.J., Sader, J.E.: Effect of surface stress on the stiffness of cantilever plates. Phys. Rev. Lett. 99, 206102 (2007)
Xu, L., Fan, H.: Torsional waves in nanowires with surface elasticity effect. Acta Mech. 227, 1783–1790 (2016)
Gurtin, M.E., Markenscoff, X., Thurston, R.N.: Effect of surface stress on the natural frequency of thin crystals. Appl. Phys. Lett. 29, 529–530 (1976)
He, Q., Lilley, C.M.: Resonant frequency analysis of Timoshenko nanowires with surface stress for different boundary conditions. J. Appl. Phys. 112, 74322 (2012)
Babaei Gavan, K., Westra, H.J.R., Van Der Drift, E.W.J.M., Venstra, W.J., Van Der Zant, H.S.J.: Size-dependent effective Young’s modulus of silicon nitride cantilevers. Appl. Phys. Lett. 94, 53–56 (2009)
Timoshenko, S.P.: LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philos. Mag. Ser. 6 41, 744–746 (1921)
Huang, Y., Zhang, M., Rong, H.W.: Buckling analysis of axially functionally graded and non-uniform beams based on Timoshenko theory. Acta Mech. Solida Sin. 29, 200–207 (2016)
He, J., Lilley, C.M.: Surface effect on the elastic behavior of static bending nanowires. Nano Lett. 8, 1798–1802 (2008)
Wang, G.-F., Feng, X.-Q.: Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Appl. Phys. Lett. 90, 231904 (2007)
Tiersten, H.F.: Linear Piezoelectric Plate Vibrations. Springer, Boston (1969)
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Xie, J., Fan, S., Chen, X. et al. Surface effects of surface nanowires on the dynamic behavior of a quartz crystal resonator under the thickness-shear mode vibrations. Acta Mech 228, 2443–2453 (2017). https://doi.org/10.1007/s00707-017-1845-0
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DOI: https://doi.org/10.1007/s00707-017-1845-0