Skip to main content
SpringerLink
Log in

Frequency dispersion of love waves in a piezoelectric nanofilm bonded on a semi-infinite elastic substrate

  • Published:
Chinese Journal of Mechanical Engineering Submit manuscript

Abstract

Research on the propagation of elastic waves in piezoelectric nanostructures is very limited. The frequency dispersion of Love waves in layered piezoelectric nanostructures has not yet been reported when surface effects are taken into account. Based on the surface elasticity theory, the propagation of Love waves with surface effects in a structure consisting of a nanosized piezoelectric film and a semi-infinite elastic substrate is investigated focusing on the frequency dispersion curves of different modes. The results show that under the electrically-open conditions, surface effects give rise to the dependence of Love wave dispersion on the film thickness when the thickness of the piezoelectric film reduces to nanometers. For a given wave frequency, phase velocity of Love waves in all dispersion modes exhibit obvious toward shift as the film thickness decreases or the surface parameters increase. Moreover, there may exist a cut-off frequency in the first mode dispersion below which Love waves will be evanescent in the structure due to surface effects. The cut-off frequency depends on the film thickness, the surface parameters and the bulk material properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. GU Bin, YU Shouwen, FENG Xiqiao. Elastic wave scattering by an interface crack between a piezoelectric layer and an elastic substrate[J]. International Journal of Fracture, 2002, 116(2): 29–34.

    Article  Google Scholar 

  2. YANG Jiashi, WANG Ji. Dynamic anti-plane problems of piezoceramics and applications in ultrasonics-A review[J]. Acta Mechanica Solida Sinica, 2008, 21(3): 207–220.

    Article  Google Scholar 

  3. PANG Yu, WANG Yuesheng, LIU Jinxi, et al. Reflection and refraction of plane waves at the interface between piezoelectric and piezomagnetic media[J]. International Journal of Engineering Science, 2009, 45: 1099–1110.

    MathSciNet  Google Scholar 

  4. GU Bin, YU Shouwen, FENG Xiqiao, et al. Scattering of love waves by an interface crack between a piezoelectric layer and an elastic substrate[J]. Acta Mechanica Solida Sinica, 2002, 15(2): 111–118.

    Google Scholar 

  5. JIN Feng, QIAN Zhenhua, WANG Zikun, et al. Propagation behavior of Love waves in a piezoelectric layered structure with inhomogeneous initial stress[J]. Smart Materials Structures, 2005, 14(4): 515.

    Article  Google Scholar 

  6. DU Jianke, JIN Xiaoying, WANG Ji, et al. Love wave propagation in functionally graded piezoelectric material layer[J]. Ultrasonics, 2007, 46(1): 13–22.

    Article  Google Scholar 

  7. DU Jianke, XIAN Kai, WANG Ji, et al. Propagation of Love waves in prestressed piezoelectric layered structures loaded with viscous liquid[J]. Acta Mechanica Solida Sinica, 2008, 21(6): 542–548.

    Article  Google Scholar 

  8. DU Jianke, XIAN Kai, WANG Ji, et al. Love wave propagation in piezoelectric layered structure with dissipation[J]. Ultrasonics, 2009, 49(2): 281–286.

    Article  Google Scholar 

  9. DU Jianke, CHENG Xiaoyu, WANG Ji, et al. The effect of viscosity on Love waves in piezoelectric structures[C]//Proceedings of the 2009 IEEE International Ultrasonics Symposium, Rome, Italy, September 20–23, 2009: 2024–2026.

    Google Scholar 

  10. LIU Jiansheng, HE Shitang. Properties of Love waves in layered piezoelectric structures[J]. International Journal of Solids and Structures, 2010, 47(2): 169–174.

    Article  MATH  Google Scholar 

  11. QIAN Zhenghua, HIROSE S. Theoretical validation on the existence of two transverse surface waves in piezoelectric/elastic layered structures[J]. Ultrasonics, 2012, 52: 442–446.

    Article  Google Scholar 

  12. MANNA S, KUNDU S, GUPTA S. Love wave propagation in a piezoelectric layer overlying in an inhomogeneous elastic half-space[J]. Journal of Vibration and Control, 2013, 1077546313513626.

    Google Scholar 

  13. GURTIN M E, MURDOCH A I. A continuum theory of elastic material surfaces[J]. Archive for Rational Mechanics Analysis, 1975, 57: 291–323.

    Article  MathSciNet  MATH  Google Scholar 

  14. GURTIN M E, WEISSMÜLLER J, LARCHE F. A general theory of curved deformable interfaces in solids at equilibrium[J]. Philisophical Magazine A, 1995, 78(5): 1093–1109.

    Article  Google Scholar 

  15. WANG Gangfeng, FENG Xiqiao, YU Shouwen. Interface effect on the diffraction of plane compressional waves by a nanosized spherical inclusion[J]. Journal of Applied Physics, 2007, 102: 043533.

    Article  Google Scholar 

  16. RU Y, WANG Gangfeng, WANG T J. Diffraction of elastic waves and stress concentration near a cylindrical nano-inclusion incorporating surface effect[J]. Journal of Vibration and Acoustics, 2009, 131: 061011–1.

    Article  Google Scholar 

  17. ZHANG Q F, WANG Gangfeng, SCHIAVONE P. Diffraction of plane compressional waves by an array of nanosized cylindrical holes[J]. Journal of Applied Mechanics, 2011, 78: 021003–1.

    Article  Google Scholar 

  18. FANG Xueqian, LIU Jinxi, YANG Shaopu, et al. Effect of surface/interface on the dynamic stress of two interacting cylindrical nano-inhomogeneities under compressional waves[J]. Thin Solid Films, 2010, 518(23): 6938–6944.

    Article  Google Scholar 

  19. PAN Xiahui, YU Shouwen, FENG Xiqiao. A continuum theory of surface piezoelectricity for nanodielectrics[J]. Science China: Physics, Mechanics & Astronomy, 2011, 54: 564–573.

    Article  Google Scholar 

  20. FANG Xueqian, LIUs Jinxi. Dynamic stress and electric displacement around a nano-fiber in piezoelectric nanocomposites under electro-elastic waves[J]. Philosophical Magazine. Letters, 2011, 91: 621–631.

    Article  Google Scholar 

  21. FANG Xueqian, LIU Jinxi, DOU Lihua, et al. Dynamic strength around two interacting piezoelectric nano-fibers with surfaces/interfaces in solid under electro-elastic waves[J]. Thin Solid Films, 2012, 520: 3587–3592.

    Article  Google Scholar 

  22. ZHANG L L, LIU Jinxi, FANG Xueqian, et al. Surface effects on the scattering of compressional waves by a piezoelectric nanocylinder[J]. Journal of Applied Physics, 2014, 115(24): 244305.

    Article  Google Scholar 

  23. ZHANG Chunli, CHEN Weiqiu, ZHANG C. On propagation of anti-plane shear waves in piezoelectric plates with surface effect[J]. Physics Letters A, 2012, 376(45): 3281–3286.

    Article  Google Scholar 

  24. CHEN Weiqiu, WU B, ZHANG Chunli, et al. On wave propagation in anisotropic elastic cylinders at nanoscale: surface elasticity and its effect[J]. Acta Mechanica, 2014, 225: 2743–2760.

    Article  MathSciNet  MATH  Google Scholar 

  25. EOM K, PARK H S, YOON D S, et al. Nanomechanical resonators and their applications in biological/chemical detection: nanomechanics principles[J]. Physics Rerports, 2011, 503: 115–163.

    Article  Google Scholar 

  26. FANG Xueqian, LIU Jinxi, GUPTA V. Fundamental formulations and recent achievements in piezoelectric nano-structures: a review[J]. Nanoscale, 2013, 5: 1716–1726.

    Article  Google Scholar 

  27. ASEMI S R, FARAJPOUR A, MOHAMMADI M. Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory[J]. Composite Structures, 2014, 116: 703–712.

    Article  Google Scholar 

  28. ASEMI H R, ASEMI S R, FARAJPOUR A, et al. Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads[J]. Physica E: Low-dimensional Systems and Nanostructures, 2015, 68: 112–122.

    Article  Google Scholar 

  29. MILLER R E, SHENOY V B. Size-dependent elastic properties of nanosized structural elements[J]. Nanotechnology, 2000, 11: 139–147.

    Article  Google Scholar 

  30. SHENOY V B. Size-dependent rigidities of nanosized torsional elements[J]. International Journal of Solids and Structures, 2002, 39: 4039–4052.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Manufacturing Science and Engineering, Southwest University of Science and Technology, Mianyang, 621010, China

    Sijia Zhang, Bin Gu, Rongying Pan &  Alamusi

  2. School of Civil Engineering and Architecture, Hainan University, Haikou, 570228, China

    Hongbin Zhang

  3. Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Xiqiao Feng

Authors
  1. Sijia Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bin Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongbin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rongying Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alamusi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xiqiao Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bin Gu.

Additional information

Supported by National Natural Science Foundation of China(Grant No. 11372261), Excellent Young Scientists Supporting Project of Science and Technology Department of Sichuan Province, China(Grant No. 2013JQ0030), Supporting Project of Department of Education of Sichuan Province, China(Grant No. 2014zd3132), Opening Project of Key Laboratory of Testing Technology for Manufacturing Process, Southwest University of Science and Technology-Ministry of Education, China(Grant No. 12zxzk02), Fund of Doctoral Research of Southwest University of Science and Technology, China(Grant No. 12zx7106), and Postgraduate Innovation Fund of Southwest University of Science and Technology, China(Grant No. 15ycx128)

ZHANG Sijia, born in 1992, is currently a graduate candidate at School of Manufacturing Science and Engineering, Southwest University of Science and Technology, China.

GU Bin, born in 1975, is currently a professor at School of Manufacturing Science and Engineering, Southwest University of Science and Technology, China. He received his PhD degree from Tsinghua University, China in 2002. His research interest covers fracture mechanics, smart materials and multi-scale computational method.

ZHANG Hongbin, born in 1973, is currently a lecturer at School of Civil Engineering and Architecture, Hainan University, China. He received his master degree from Tsinghua University, China in 1999. His research focuses on modeling and numerical simulation on multi-physics coupling field problems.

PAN Rongying, born in 1991, is currently a graduate candidate at School of Manufacturing Science and Engineering, Southwest University of Science and Technology, China.

Alamusi, born in 1978, is currently an associate professor at School of Manufacturing Science and Engineer, Southwest University of Science and Technology, China. He received his PhD degree from Chiba University, Japan in 2013. His research is mainly on the development and applications of functional nanocomposites.

FENG Xiqiao, born in 1968, is currently the director of Institute of Biomechanics and Medical Engineering, Tsinghua University, China. He received his PhD degree from Tsinghua University, China in 1995. His research fields include biological mechanics, micro mechanics of cell damage and fracture mechanics.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, S., Gu, B., Zhang, H. et al. Frequency dispersion of love waves in a piezoelectric nanofilm bonded on a semi-infinite elastic substrate. Chin. J. Mech. Eng. 28, 1157–1162 (2015). https://doi.org/10.3901/CJME.2015.0709.090

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3901/CJME.2015.0709.090

Keywords

Search

Navigation