Cluster Computing

, Volume 22, Supplement 2, pp 4157–4163 | Cite as

Eigen vector buckling based boundary analysis method for free vibration of rectangular thin plates

  • Hongwang ZhaoEmail author
  • Aicheng Zou


The main research topic of this paper is the application of the finite element method boundary analysis theory to study the stability of plate in irregular shape. First of all, the basic theory of free vibration of elastic plate and the basic equations of elastodynamics are introduced, and the governing equation of small deflection of free vibration of plate is given. Secondly, the finite element method boundary analysis method is introduced in details, including the basic idea and analysis steps of finite element method boundary analysis, and some element types, so as to lay a theoretical foundation for better understanding of finite element method boundary analysis method and application of it to analyze the stability of plate. At last, finite element method boundary analysis is applied to analyze the stability of plate, among which, the structural analysis types in ANSYS software and its analysis steps are introduced, and buckling (eigenvalues) analysis in ANSYS software is mainly introduced, and the effective performance of algorithm is verified by applying ANSYS software.


Rectangular plate Free vibration Finite element method boundary analysis Boundary analysis 



This work is carried out with the support of Guanxi junior high school teachers’ basic ability improvement project “Optimization of thin plate vibration problems with lumped mass based on modal analysis”(KY2016YB530). Guangxi Natural Science Foundation under Grant No. 2016GXNSFBA380230)


  1. 1.
    Han, W., Petyt, M.: Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method–II: 1st mode of laminated plates and higher modes of isotropic and laminated plates. Comput. Struct. 63(2), 309–318 (1997)Google Scholar
  2. 2.
    Altunsaray, E., Bayer, İ.: Deflection and free vibration of symmetrically laminated quasi-isotropic thin rectangular plates for different boundary conditions. Ocean Eng. 57, 197–222 (2013)Google Scholar
  3. 3.
    Taazount, M., Zinai, A., Bouazzouni, A.: Large free vibration of thin plates: hierarchic finite element method and asymptotic linearization. Eur. J. Mech.- A/Solids 28(1), 155–165 (2009)Google Scholar
  4. 4.
    Semnani, S.J., Attarnejad, R., Firouzjaei, R.K.: Free vibration analysis of variable thickness thin plates by two-dimensional differential transform method. Acta Mechanica 224(8), 1643–1658 (2013)Google Scholar
  5. 5.
    Chen, J.T., Chen, I.L., Chen, K.H., et al.: A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function. Eng. Anal. Bound. Elements 28(5), 535–545 (2004)Google Scholar
  6. 6.
    Nguyen-Xuan, H., Tran, L.V., Thai, C.H., et al.: Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing. Thin-Walled Struct. 54, 1–8 (2012)Google Scholar
  7. 7.
    Xiang, Y., Lai, S.K., Zhou, L.: DSC-element method for free vibration analysis of rectangular mindlin plates. Int. J. Mech. Sci. 52(4), 548–560 (2010)Google Scholar
  8. 8.
    Chen, L., Liu, G.R., Jiang, Y., et al.: A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media. Eng. Fract. Mech. 78(1), 85–109 (2011)Google Scholar
  9. 9.
    Eftekhari, S.A., Jafari, A.A.: A simple and accurate Ritz formulation for free vibration of thick rectangular and skew plates with general boundary conditions. Acta Mechanica 224(1), 193–209 (2013)Google Scholar
  10. 10.
    Ma, Y., Zhang, Y., Kennedy, D.: A symplectic analytical wave based method for the wave propagation and steady state forced vibration of rectangular thin plates. J. Sound Vib. 339(4), 196–214 (2015)Google Scholar
  11. 11.
    Shi, X., Shi, D., Li, W.L., et al.: A unified method for free vibration analysis of circular, annular and sector plates with arbitrary boundary conditions. J. Vib. Control 22, 442–456 (2016)Google Scholar
  12. 12.
    Jin, C., Wang, X.: Weak form quadrature element method for accurate free vibration analysis of thin skew plates. Comput. Math. Appl. 70(8), 2074–2086 (2015)Google Scholar
  13. 13.
    Shi, D., Wang, Q., Shi, X., et al.: Free vibration analysis of moderately thick rectangular plates with variable thickness and arbitrary boundary conditions. Shock Vib. 1, 1–25 (2014)Google Scholar
  14. 14.
    Jin, C., Wang, X.: Weak form quadrature element method for accurate free vibration analysis of thin skew plates. Comput. Math. Appl. 70, 2074–2086 (2015)Google Scholar
  15. 15.
    Hamza, R., Muhammad, K., Arunkumar, N., González, G.R.: Hash based encryption for keyframes of diagnostic hysteroscopy. IEEE Access (2017).

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Guilin University of Aerospace TechnologyGuilinChina

Personalised recommendations