Skip to main content
SpringerLink
Log in

Buckling of a Reissner–Mindlin plate of piezoelectric semiconductors

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

We study the buckling of a Reissner–Mindlin plate of piezoelectric semiconductors. A set of two-dimensional equations is established. The pre-buckling state is determined by the zero-order plate equations for in-plane extension/compression. The buckling state is governed by the first-order plate equations for bending with shear deformation. A rectangular plate is analyzed using bi-sinusoidal trigonometric series. The buckling loads and modes are obtained. It is shown that piezoelectric coupling exhibits a stiffening effect and raises the buckling load. At the same time semiconduction reduces the piezoelectric stiffening effect because of the screening effect of the mobile charges. The mobile charges assume various in-plane distributions in different buckling modes. Buckling loads and modes of circular plates are also presented.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data availability statement

The data that supports the findings of this study are available within the article.

References

  1. Cady WG (1946) Piezoelectricity. McGraw-Hill, New York

    Google Scholar 

  2. Tiersten HF (1969) Linear piezoelectric plate vibrations. Plenum, New York

    Book  Google Scholar 

  3. Meitzler AH, Berlincourt D, Welsh FS III, Tiersten HF, Coquin GA, Warner AW (1988) IEEE standard on piezoelectricity. IEEE, New York. https://doi.org/10.1109/IEEESTD.1988.79638

    Article  Google Scholar 

  4. Hickernell FS (2005) The piezoelectric semiconductor and acoustoelectronic device development in the sixties. IEEE Trans Ultrason Ferroelec Freq Contr 52(5):737–745. https://doi.org/10.1109/TUFFC.2005.1503961

    Article  Google Scholar 

  5. Ballato A (2000) Piezoelectric excitation of semiconductor plates. Ultrasonics 38:849–851. https://doi.org/10.1016/S0041-624X(99)00100-6

    Article  Google Scholar 

  6. Wang ZL, Wu WZ (2014) Piezotronics and piezo-phototronics: fundamentals and applications. Natl Sci Rev 1:62–90. https://doi.org/10.1093/nsr/nwt002

    Article  Google Scholar 

  7. Liu Y, Zhang Y, Yang Q, Niu SM, Wang ZL (2015) Fundamental theories of piezotronics and piezo-phototronics. Nano Energy 14:257–275. https://doi.org/10.1016/j.nanoen.2014.11.051

    Article  Google Scholar 

  8. Wang ZL, Wu WZ, Falconi C (2018) Piezotronics and piezophototronics with third generation semiconductors. MRS Bull 43:922–927. https://doi.org/10.1557/mrs.2018.263

    Article  Google Scholar 

  9. Zhang Y, Leng YS, Willatzen M, Huang BL (2018) Theory of piezotronics and piezophototronics. MRS Bull 43:928–935. https://doi.org/10.1557/mrs.2018.297

    Article  Google Scholar 

  10. Wang ZL (2012) Piezotronics and piezo-phototronics. Springer, Berlin

    Book  Google Scholar 

  11. Wauer J, Suherman S (1997) Thickness vibrations of a piezo-semiconducting plate layer. Int J Eng Sci 35:1387–1404. https://doi.org/10.1016/s0020-7225(97)00060-8

    Article  MATH  Google Scholar 

  12. Jiao FY, Wei PJ, Zhou YH, Zhou XL (2019) Wave propagation through a piezoelectric semiconductor slab sandwiched by two piezoelectric half-spaces. Eur J Mech A Solids 75:70–81. https://doi.org/10.1016/j.euromechsol.2019.01.007

    Article  MathSciNet  MATH  Google Scholar 

  13. Jiao FY, Wei PJ, Zhou YH, Zhou XL (2019) The dispersion and attenuation of the multi-physical fields coupled waves in a piezoelectric semiconductor. Ultrasonics 92:68–78. https://doi.org/10.1016/j.ultras.2018.09.009

    Article  Google Scholar 

  14. Tian R, Liu JX, Pan E, Wang YS, Soh AK (2019) Some characteristics of elastic waves in a piezoelectric semiconductor plate. J Appl Phys 126:125701. https://doi.org/10.1063/1.5116662

    Article  Google Scholar 

  15. Sladek J, Sladek V, Pan E, Wuensche M (2014) Fracture analysis in piezoelectric semiconductors under a thermal load. Eng Fract Mech 126:27–39. https://doi.org/10.1016/j.engfracmech.2014.05.011

    Article  Google Scholar 

  16. Zhao MH, Pan YB, Fan CY, Xu GT (2016) Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors. Int J Solids Struct 94–95:50–59. https://doi.org/10.1016/j.ijsolstr.2016.05.009

    Article  Google Scholar 

  17. Qin GS, Lu CS, Zhang X, Zhao MH (2018) Electric current dependent fracture in GaN piezoelectric semiconductor ceramics. Materials 11:2000. https://doi.org/10.3390/ma11102000

    Article  Google Scholar 

  18. Afraneo R, Lovat G, Burghignoli P, Falconi C (2012) Piezo-semiconductive quasi-1D nanodevices with or without anti-symmetry. Adv Mater 24:4719–4724. https://doi.org/10.1002/adma.201104588

    Article  Google Scholar 

  19. Fan SQ, Liang YX, Xie JM, Hu YT (2017) Exact solutions to the electromechanical quantities inside a statically-bent circular ZnO nanowire by taking into account both the piezoelectric property and the semiconducting performance: part I-Linearized analysis. Nano Energy 40:82–87. https://doi.org/10.1016/j.nanoen.2017.07.049

    Article  Google Scholar 

  20. Liang YX, Fan SQ, Chen XD, Hu YT (2018) Nonlinear effect of carrier drift on the performance of an n-type ZnO nanowire nanogenerator by coupling piezoelectric effect and semiconduction. Nanotechnology 9:1917–1925. https://doi.org/10.3762/bjnano.9.183

    Article  Google Scholar 

  21. Zhang CL, Luo YX, Cheng RR, Wang XY (2017) Electromechanical fields in piezoelectric semiconductor nanofibers under an axial force. MRS Adv 2:3421–3426. https://doi.org/10.1557/adv.2017.301

    Article  Google Scholar 

  22. Yang JS (2020) Analaysis of piezoelectric semiconductor structures. Springer Nature, Cham

  23. Yang JS (1998) Equations for the extension and flexure of a piezoelectric beam with rectangular cross section and applications. Int J Appl Electromagn Mech 9:409–420. https://doi.org/10.3233/JAEM-1998-121

    Article  Google Scholar 

  24. Hu YT, Yang JS, Jiang Q (2002) Characterization of electroelastic beams under biasing fields with applications in buckling analysis. Arch Appl Mech 72:439–450. https://doi.org/10.1007/s00419-001-0197-2

    Article  MATH  Google Scholar 

  25. Kiani Y, Rezaei M, Taheri S et al (2011) Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams. Int J Mech Mater Des 7:185–197. https://doi.org/10.1007/s10999-011-9158-2

    Article  Google Scholar 

  26. Yan Z, Jiang LY (2011) The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects. Nanotechnology 22:245703. https://doi.org/10.1088/0957-4484/22/24/245703

    Article  Google Scholar 

  27. Liang C, Zhang C, Chen W, Yang JS (2020) Static buckling of piezoelectric semiconductor fibers. Mater Res Express 6:125919. https://doi.org/10.1088/2053-1591/ab663b

    Article  Google Scholar 

  28. Yang JS (1998) Buckling of a piezoelectric plate. Int J Appl Electromagn Mech 9:399–408. https://doi.org/10.3233/JAEM-1998-120

    Article  Google Scholar 

  29. Hu YT, Yang JS, Jiang Q (2002) A model of electroelastic plates under biasing fields with applications in buckling analysis. Int J Solids Struct 39:2629–2642. https://doi.org/10.1016/S0020-7683(02)00122-1

    Article  MATH  Google Scholar 

  30. Zhang J, Wang CY, Adhikari S (2012) Surface effect on the buckling of piezoelectric nanofilms. J Phys D: Appl Phys 45:285301. https://doi.org/10.1088/0022-3727/45/28/285301

    Article  Google Scholar 

  31. Shen HS (2009) A comparison of buckling and postbuckling behavior of FGM plates with piezoelectric fiber reinforced composite actuators. Compos Struct 91:375–384. https://doi.org/10.1016/j.compstruct.2009.06.005

    Article  Google Scholar 

  32. Jabbari M, Joubaneh EF, Khorshidv AR, Eslami MR (2013) Buckling analysis of porous circular plate with piezoelectric actuator layers under uniform radial compression. Int J Mech Sci 70:50–56. https://doi.org/10.1016/j.ijmecsci.2013.01.031

    Article  Google Scholar 

  33. Barati MR, Sadr MH, Zenkour AM (2016) Buckling analysis of higher order graded smart piezoelectric plates with porosities resting on elastic foundation. Int J Mech Sci 117:309–320. https://doi.org/10.1016/j.ijmecsci.2016.09.012

    Article  Google Scholar 

  34. Mao JJ, Zhang W (2019) Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces. Compos Struct 216:392–405. https://doi.org/10.1016/j.compstruct.2019.02.095

    Article  Google Scholar 

  35. Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill, New York

    Google Scholar 

  36. Sze SM (2006) Physics of semiconductor devices. Wiley, New York

    Book  Google Scholar 

  37. Auld BA (1973) Acoustic fields and waves in solids. Wiley, New York

    Google Scholar 

  38. Masliyah JH, Bhattacharjee S (2006) Electrokinetic and colloid transport phenomena. Wiley, New York, pp 105–178

    Book  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China [No. 12072253, Feng Jin]; 111 Project version 2.0 [Feng Jin]; and the Fundamental Research Funds for the Central Universities [No. xzy022020016, Yilin Qu].

Author information

Authors and Affiliations

  1. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Yilin Qu & Feng Jin

  2. Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68588-0526, USA

    Jiashi Yang

Authors
  1. Yilin Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiashi Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Feng Jin or Jiashi Yang.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qu, Y., Jin, F. & Yang, J. Buckling of a Reissner–Mindlin plate of piezoelectric semiconductors. Meccanica 57, 2797–2807 (2022). https://doi.org/10.1007/s11012-022-01598-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-022-01598-2

Keywords

Search

Navigation