Skip to main content
SpringerLink
Log in

Dynamic Stiffness Formulation for Vibration of FGM Stepped Annular Plates of Varying Thickness with Non-homogenous Material

  • Conference paper
  • First Online:
Advances in Engineering Research and Application (ICERA 2019)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 104))

Included in the following conference series:

  • 920 Accesses

Abstract

The article introduces a new continuous element (CE) for free vibration analysis of stepped functionally graded materials (FGMs) annular plates having non-homogenous material properties and varying thickness subjected to arbitrary boundary conditions. By applying the powerful assembly capacity of CE method, the dynamic stiffness matrix for the stepped FGMs annular plates with non-homogenous properties has been established. Continuous Element Method allows computing the natural frequencies with high accuracy for any frequency range where almost other current methods meet grand difficulties due to the number of meshing elements. Using minimum meshing for complex structures, this model accelerates the speed of computation and economies the storage capacity of computers.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Hosseini-Hashemi, S., Derakhshani, M., Fadaee, M.: An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates. Appl. Math. Model. 37, 4147–4164 (2013)

    Article  MathSciNet  Google Scholar 

  2. Tornabene, F.: Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution. Comput. Methods Appl. Mech. Eng. 198, 2911–2935 (2009)

    Article  Google Scholar 

  3. Tahouneh, V., Yas, M.H.: 3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method. Acta Mech. 223, 1879–1897 (2012)

    Article  MathSciNet  Google Scholar 

  4. Efraim, E., Eisenberger, M.: Exact vibration analysis of variable thickness thick annular isotropic and FGM plates. J. Sound Vib. 299, 720–738 (2007)

    Article  Google Scholar 

  5. Hosseini-Hashemi, S., Es’haghi, M., Karimi, M.: Closed-form vibration analysis of thick annular functionally graded plates with integrated piezoelectric layers. Int. J. Mech. Sci. 52, 410–428 (2010)

    Article  Google Scholar 

  6. Nie, G.J., Zhong, Z.: Dynamic analysis of multi-directional functionally graded annular plates. Appl. Math. Modell. 34, 608–616 (2010)

    Article  MathSciNet  Google Scholar 

  7. Dong, C.Y.: Three-dimensional free vibration analysis of functionally graded annular plates using the Chebyshev-Ritz method. Mater. Des. 29, 1518–1525 (2008)

    Article  Google Scholar 

  8. Su, Z., Jin, G.Y., Shi, S.X., Ye, T.G., Jia, X.Z.: A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions. Int. J. Mech. Sci. 80, 62–80 (2014)

    Article  Google Scholar 

  9. Xie, X., Jin, G.Y., Ye, T.G., Liu, Z.G.: Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method. Appl. Acoust. 85, 130–142 (2014)

    Article  Google Scholar 

  10. Casimir, J.B., Nguyen, M.C., Tawfig, I.: Thick shells of revolution: derivation of the dynamic stiffness matrix of continuous elements and application to a tested cylinder. Comput. Struct. 85, 1845–1857 (2007)

    Article  Google Scholar 

  11. Thinh, T.I., Cuong, N.M., Ninh, D.G.: Dynamic stiffness formulation for vibration analysis of thick composite plates resting on non-homogenous foundations. Compos. Struct. 108, 684–695 (2014)

    Article  Google Scholar 

  12. Reddy, J.N.: Mechanics of Laminated Composites Plates and Shells. CRC Press, New York (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Viet Tri University of Industry, Viet Tri, Vietnam

    Le Quang Vinh

  2. Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Nguyen Dong Anh

  3. School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam

    Nguyen Manh Cuong

Authors
  1. Le Quang Vinh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nguyen Dong Anh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nguyen Manh Cuong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Le Quang Vinh .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Automation, TU Ilmenau, Ilmenau, Thüringen, Germany

    Kai-Uwe Sattler

  2. Faculty of Electronic Engineering, Thai Nguyen University of Technology, Thai Nguyen, Vietnam

    Duy Cuong Nguyen

  3. Faculty of Mechanical Engineering, Thai Nguyen University of Technology, Thai Nguyen, Vietnam

    Ngoc Pi Vu

  4. Hanoi University of Science and Technology, Hanoi, Vietnam

    Banh Tien Long

  5. Institute for Automation and Systems Engineering, TU Ilmenau, Ilmenau, Thüringen, Germany

    Horst Puta

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Vinh, L.Q., Anh, N.D., Cuong, N.M. (2020). Dynamic Stiffness Formulation for Vibration of FGM Stepped Annular Plates of Varying Thickness with Non-homogenous Material. In: Sattler, KU., Nguyen, D., Vu, N., Tien Long, B., Puta, H. (eds) Advances in Engineering Research and Application. ICERA 2019. Lecture Notes in Networks and Systems, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-030-37497-6_31

Download citation

Publish with us

Policies and ethics

Search

Navigation