Skip to main content
SpringerLink
Log in

Exact axisymmetric solutions for laminated transversely isotropic piezoelectric circular plate (I)

Exact solutions for piezoelectric circular plate

  • Published:
Science in China Series E: Technological Sciences Aims and scope Submit manuscript

Abstract

Based on three-dimensional elastic equations for piezoelectric materials, the state equations for piezoelectric circular plate under axisymmetric deformation are derived. Applying Hankel transform to them and letting the free boundary terms resulting from Hankel transform be zero, a set of ordinary differential equations with constant coefficients and associated boundary conditions are obtained. Furthermore, two exact solutions corresponding to generalized rigid slipping and generalized elastic simple support are deduced. Then, the governing equations obtained reduce to equations for axisymmetric problem of transversely isotropic circular plate. Under the two types of boundary conditions of elastic simple support and rigid slipping, exact solutions are derived. Finally, numerical results are presented and applicability of the classical plate theory is discussed.

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. Sosa, H., On the modeling of piezoelectric laminated structures,Mech. Res. Commun., 1992, 19: 541.

    Article  MATH  Google Scholar 

  2. Jiang, L. Z., Lee, J. S., Discussion on “On the modeling of piezoelectric laminated structures”,Mech. Res. Commun., 1993, 20: 437.

    Article  Google Scholar 

  3. Lee, J. S., Jiang, L. Z., Exact electroelastic analysis of piezoelectric laminae via state space approach,Int. J. Solids Structures, 1996, 33: 977.

    Article  MATH  Google Scholar 

  4. Bahar, L. Y., Discussion on “A mixed method in elasticity”,J. Appl. Mech., 1977, 44: 790.

    Google Scholar 

  5. Pagano, N. J., Exact solutions for rectangular bidirectional composites and sandwich plates,J. Composite Materials, 1970, 4: 20.

    Google Scholar 

  6. Srinivas, S., Rao, A. K., Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates,Int. J. Solids Structures, 1970, 6: 1463.

    Article  MATH  Google Scholar 

  7. Chen, W. Q., Liang, J., Ding, H. J., Three dimensional analysis of bending problems of thick piezoelectric composite rectangular plates,Acta Materiae Compositae Sinica, 1997, 14: 108.

    Google Scholar 

  8. Timoshenko, S., Goodier, J. N.,Theory of Elasticity, 3rd ed., New York: McGraw-Hill, 1951.

    MATH  Google Scholar 

  9. Sneddon, I. N.,Fourier Transforms, New York: McGraw-Hill, 1951.

    Google Scholar 

  10. Deif, A. S.,Advanced Matrix Theory for Scientists and Engineers, New York: Abacus Press-Halsted Press, 1982, 108–110.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Zhejiang University, 310027, Hangzhou, China

    Haojiang Ding, Rongqiao Xu & Fenglin Guo

Authors
  1. Haojiang Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rongqiao Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fenglin Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 19572059) and the Research Laboratory of Solid Mechanics of State Education Commission of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, H., Xu, R. & Guo, F. Exact axisymmetric solutions for laminated transversely isotropic piezoelectric circular plate (I). Sci. China Ser. E-Technol. Sci. 42, 388–395 (1999). https://doi.org/10.1007/BF02916748

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02916748

Keywords

Search

Navigation