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Propagation of Rayleigh-type surface waves in a layered piezoelectric nanostructure with surface effects

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Abstract

This work investigates the dispersion properties of Rayleigh-type surface waves propagating in a layered piezoelectric nanostructure composed of a piezoelectric nanofilm over an elastic substrate. As one of the most important features of nanostructures, surface effects characterized by surface stresses and surface electric displacements are taken into account through the surface piezoelectricity theory and the nonclassical mechanical and electrical boundary conditions. Concrete expressions of the dispersion equation are derived, and numerical results are provided to examine the effects of several surface-related parameters, including the surface elasticity, surface piezoelectricity, surface dielectricity, surface density, as well as surface residual stress, on the dispersion modes and phase velocity. The size-dependent dispersion behaviors occurring with surface effects are also predicted, and they may vanish once the thickness of the piezoelectric nanofilm reaches a critical value.

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References

  1. XU, S. Y., POIRIER, G., and YAO, N. PMN-PT nanowires with a very high piezoelectric constant. Nano Letters, 12(5), 2238–2242 (2012)

    Article  Google Scholar 

  2. XU, S. Y., YEH, Y. W., POIRIER, G., MCALPINE, M. C., REGISTER, R. A., and YAO, N. Flexible piezoelectric PMN-PT nanowire-based nanocomposite and device. Nano Letters, 13(6), 2393–2398 (2013)

    Article  Google Scholar 

  3. XU, S., QIN, Y., XU, C., WEI, Y. G., YANG, R. S., and WANG, Z. L. Self-powered nanowire devices. Nature Nanotechnology, 5(5), 366–373 (2010)

    Article  Google Scholar 

  4. WANG, X. D., SONG, J. H., LIU J., and WANG, Z. L. Direct-current nanogenerator driven by ultrasonic waves. Science, 316(5821), 102–105 (2007)

    Article  Google Scholar 

  5. ZHOU, J., GU, Y. D., FEI, P., MAI, W. J., GAO, Y. F., YANG, R. S., BAO, G., and WANG, Z. L. Flexible piezotronic strain sensor. Nano Letters, 8(9), 3035–3040 (2008)

    Article  Google Scholar 

  6. WU, J. M., CHEN, C. Y., ZHANG, Y., CHEN, K. H., YANG, Y., HU, Y. F., HE, J. H., and WANG, Z. L. Ultrahigh sensitive piezotronic strain sensors based on a ZnSnO3 nanowire/microwire. ACS Nano, 6(5), 4369–4374 (2012)

    Article  Google Scholar 

  7. TANNER, S. M., GRAY, J. M., ROGERS, C. T., BERTNESS, K. A., and SANFORD, N. A. High-Q GaN nanowire resonators and oscillators. Applied Physics Letters, 91(20), 203117 (2007)

    Article  Google Scholar 

  8. TRIVEDI, S. and NEMADE, H. B. Simulation of a Love wave device with ZnO nanorods for high mass sensitivity. Ultrasonics, 84, 150–161 (2018)

    Article  Google Scholar 

  9. WANG, X. D., ZHOU, J., SONG, J. H., LIU, J., XU, N. S., and WANG, Z. L. Piezoelectric field effect transistor and nanoforce sensor based on a single ZnO nanowire. Nano Letters, 6(12), 2768–2772 (2006)

    Article  Google Scholar 

  10. HE, J. H., HSIN, C. L., LIU, J., CHEN, L. J., and WANG, Z. L. Piezoelectric gated diode of a single ZnO nanowire. Advanced Materials, 19(6), 781–784 (2007)

    Article  Google Scholar 

  11. AGRAWAL, R., PENG, B., GDOUTOS, E. E., and ESPINOSA, H. D. Elasticity size effects in ZnO nanowires-a combined experimental-computational approach. Nano Letters, 8(11), 3668–3674 (2008)

    Article  Google Scholar 

  12. CHEN, C. Q., SHI, Y., ZHANG, Y. S., ZHU, J., and YAN, Y. J. Size dependence of Young’s modulus in ZnO nanowires. Physical Review Letters, 96(7), 075505 (2006)

    Article  Google Scholar 

  13. DAI, S. X. and PARK, H. S. Surface effects on the piezoelectricity of ZnO nanowires. Journal of Mechanics and Physics of Solids, 61(2), 385–397 (2013)

    Article  Google Scholar 

  14. HOANG, M. T., YVONNET, J., MITRUSHCHENKOV, A., and CHAMBAUD, G. First-principles based multiscale model of piezoelectric nanowires with surface effects. Journal of Applied Physics, 113(1), 014309 (2013)

    Article  Google Scholar 

  15. QIAN, D. H. Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects. Applied Mathematics and Mechanics (English Edition), 41(3), 425–438 (2020) https://doi.org/10.1007/s10483-020-2586-5

    Article  MathSciNet  Google Scholar 

  16. FANG, X. Q., LIU, J. X., and GUPTA, V. Fundamental formulations and recent achievements in piezoelectric nano-structures: a review. Nanoscale, 5(5), 1716–1726 (2013)

    Article  Google Scholar 

  17. YAN, Z. and JIANG, L. Y. Modified continuum mechanics modeling on size-dependent properties of piezoelectric nanomaterials: a review. Nanomaterials, 7(2), 27 (2017)

    Article  MathSciNet  Google Scholar 

  18. HONG, J., HE, Z., ZHANG, G., and MI, C. Size and temperature effects on band gaps in periodic fluid-filled micropipes. Applied Mathematics and Mechanics (English Edition), 42(9), 1219–1232 (2021) https://doi.org/10.1007/s10483-021-2769-8

    Article  MathSciNet  Google Scholar 

  19. GURTIN, M. E. and MURDOCH, A. I. A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 57(4), 291–323 (1975)

    Article  MathSciNet  Google Scholar 

  20. WANG, J. X., HUANG, Z. P., DUAN, H. L., YU, S. W., FENG, X. Q., WANG, G. F., ZHANG, W. X., and WANG, T. J. Surface stress effect in mechanics of nanostructured materials. Acta Mechanica Solida Sinica, 24(1) 52–82 (2011)

    Article  Google Scholar 

  21. HUANG, G. Y. and YU, S. W. Effect of surface piezoelectricity on the electromechanical behavior of a piezoelectric ring. Physica Status Solidi B: Basic Solid State Physics, 243(4) 22–24 (2006)

    Article  Google Scholar 

  22. PAN, X. H., YU, S. W., and FENG, X. Q. A continuum theory of surface piezoelectricity for nanodielectrics. SCIENCE CHINA Physics Mechanics & Astronomy, 54(4), 564–573 (2011)

    Article  Google Scholar 

  23. XIAO, J. H., XU, Y. L., and ZHANG, F. C. Evaluation of effective electroelastic properties of piezoelectric coated nano-inclusion composites with interface effect under antiplane shear. International Journal of Engineering Science, 69, 61–68 (2013)

    Article  Google Scholar 

  24. FANG, X. Q., YANG, Q., LIU, J. X., and FENG, W. J. Surface/interface effect around a piezoelectric nano-particle in a polymer matrix under compressional waves. Applied Physics Letters, 100(15), 151602 (2012)

    Article  Google Scholar 

  25. ZHANG, L. L., LIU, J. X., FANG, X. Q., and NIE, G. Q. Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects. Physica E, 57, 169–174 (2014)

    Article  Google Scholar 

  26. ZHANG, C. L., CHEN, W. Q., and ZHANG, C. On propagation of anti-plane shear waves in piezoelectric plates with surface effect. Physics Letters A, 376(45), 3281–3286 (2012)

    Article  Google Scholar 

  27. YAN, Z. and JIANG, L. Y. Surface effects on the electromechanical coupling and bending behaviours of piezoelectric nanowires. Journal of Physics D: Applied Physics, 44(7), 075404 (2011)

    Article  Google Scholar 

  28. YAN, Z. and JIANG, L. Y. The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects. Nanotechnology, 22(24), 245703 (2011)

    Article  Google Scholar 

  29. ZHANG, J., WANG, C. Y., and ADHIKARI, S. Surface effect on the buckling of piezoelectric nanofilms. Journal of Physics D: Applied Physics, 45(28), 285301 (2012)

    Article  Google Scholar 

  30. ZHANG, J. and WANG, C. Y. Vibrating piezoelectric nanofilms as sandwich nanoplates. Journal of Applied Physics, 111(9), 094303 (2012)

    Article  Google Scholar 

  31. LI, Y. H., FANG, B., ZHANG, J. H., and SONG, J. Z. Surface effects on the wrinkling of piezoelectric films on compliant substrates. Journal of Applied Physics, 110(11), 114303 (2011)

    Article  Google Scholar 

  32. GUO, X. and WEI, P. J. Dispersion relations of in-plane elastic waves in nano-scale one dimensional piezoelectric semiconductor/piezoelectric dielectric phononic crystal with the consideration of interface effect. Applied Mathematical Modelling, 96, 189–214 (2021)

    Article  MathSciNet  Google Scholar 

  33. HUANG, Y., DAS, P. K., and BHETHANABOTLA, V. R. Surface acoustic waves in biosensing applications. Sensors and Actuators Reports, 3, 100041 (2021)

    Article  Google Scholar 

  34. YANG, W. J., LIANG, X., and SHEN, S. P. Love waves in layered flexoelectric structures. Philosophical Magazine, 97(33), 3186–3209 (2017)

    Article  Google Scholar 

  35. WANG, X., LI, P., and JIN, F. A generalized dynamic model of nanoscale surface acoustic wave sensors and its applications in Love wave propagation and shear-horizontal vibration. Applied Mathematical Modelling, 75, 101–115 (2019)

    Article  MathSciNet  Google Scholar 

  36. CHEN, T. Y., CHIU, M. S., and WENG, C. N. Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. Journal of Applied Physics, 100(7), 074308 (2006)

    Article  Google Scholar 

  37. YANG, J. S. Analysis of Piezoelectric Devices, World Scientific Publishing, Hackensack (2006)

    Book  Google Scholar 

  38. BENETTI, M., CANNATA, D., DI-PIETRANTONIO, F., and VERONA, E. Growth of ALN piezoelectric film on diamond for high-frequency surface acoustic wave devices. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 52(10), 1806–1811 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Lele Zhang, Guoquan Nie & Jinxi Liu

  2. Hebei Key Laboratory of Mechanics of Intelligent Materials and Structures, Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Lele Zhang, Guoquan Nie & Jinxi Liu

  3. Department of Architecture, Shijiazhuang Institute of Railway Technology, Shijiazhuang, 050041, China

    Jing Zhao

Authors
  1. Lele Zhang
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  2. Jing Zhao
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  3. Guoquan Nie
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  4. Jinxi Liu
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Correspondence to Jinxi Liu.

Additional information

Citation: ZHANG, L. L., ZHAO, J., NIE, G. Q., and LIU, J. X. Propagation of Rayleigh-type surface waves in a layered piezoelectric nanostructure with surface effects. Applied Mathematics and Mechanics (English Edition), 43(3), 327–340 (2022) https://doi.org/10.1007/s10483-022-2824-7

Project supported by the National Natural Science Foundation of China (Nos. 11802185 and 11872041), the Natural Science Foundation of Hebei Province of China (No. A2019210203), and the Youth Fund Project of Hebei Education Department of China (No. QN2018037)

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Zhang, L., Zhao, J., Nie, G. et al. Propagation of Rayleigh-type surface waves in a layered piezoelectric nanostructure with surface effects. Appl. Math. Mech.-Engl. Ed. 43, 327–340 (2022). https://doi.org/10.1007/s10483-022-2824-7

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  • DOI: https://doi.org/10.1007/s10483-022-2824-7

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