Skip to main content
SpringerLink
Log in
Book cover

Haar Wavelets pp 177–187Cite as

Vibrations of Functionally Graded Timoshenko Beams

  • Chapter
  • First Online:

  • 2086 Accesses

Part of the book series: Mathematical Engineering ((MATHENGIN))

Abstract

Consider an axially graded Timoshenko beam of length L with a variable cross-section subjected to a constant compressive load P.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

References

  1. Auciello, N., Ercolano, A.: A general solution for dynamic response of axially loaded non-uniform Timoshenko beams. Int. J. Solids Struct. 41, 4861–4874 (2004)

    Article  MATH  Google Scholar 

  2. Feklistova, L., Hein, H.: Free vibration and stability analysis of functionally graded Timoshenko beams. In: Pimenta, P. (ed.) 10th World Congress of Computational Mechanics (2012)

    Google Scholar 

  3. Filipich, C., Cortinez, M.: Natural frequencies of a Timoshenko beam: exact values by means of a generalized solution. Mecanica Computadonal 14, 134–143 (1994)

    Google Scholar 

  4. Gunda, J., Gupta, R., Janardhan, G., Rao, G.: Large amplitude vibration analysis of composite beams: simple closed-form solutions. Compos. Struct. 93, 870–879 (2011)

    Article  Google Scholar 

  5. Hemmatnezhad, M., Ansari, R., Rahimi, G.: Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation. Appl. Math. Model. 37, 8495–8504 (2013)

    Google Scholar 

  6. Huang, Y., Li, X.: A new approach for free vibration of axially functionally graded beams with non-uniform cross-section. J. Sound Vib. 329, 2291–2303 (2010)

    Article  Google Scholar 

  7. Huang, Y., Yang, L., Luo, Q.: Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section. Compos. B Eng. 45, 1493–1498 (2013)

    Article  Google Scholar 

  8. Li, S., Batra, R.: Relations between buckling loads of functionally graded Timoshenko and homogeneous EulerBernoulli beams. Compos. Struct. 95, 5–9 (2013)

    Google Scholar 

  9. Li, X.: A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and EulerBernoulli beams. J. Sound Vib. 318, 1210–1229 (2008)

    Google Scholar 

  10. Liao, M., Zhong, H.: Nonlinear vibration analysis of tapered Timoshenko beams. Chaos, Solitons Fractals 36, 1267–1272 (2008)

    Article  MATH  Google Scholar 

  11. Mo, Y., Ou, L., Zhong, H.: Vibration analysis of Timoshenko beams on a nonlinear elastic foundation. Tsinghua Sci. Technol. 14, 322–326 (2009)

    Article  MathSciNet  Google Scholar 

  12. Mohanty, S., Dash, R., Rout, T.: Parametric instability of a functionally graded Timoshenko beam on Winkler’s elastic foundation. Nucl. Eng. Des. 241, 2698–2715 (2011)

    Article  Google Scholar 

  13. Morfidis, K.: Vibration of Timoshenko beams on three-parameter elastic foundation. Comput. Struct. 88, 294–308 (2010)

    Article  Google Scholar 

  14. Pradhan, K., Chakraverty, S.: Free vibration of Euler and Timoshenko functionally graded beams by RayleighRitz method. Compos. B Eng. 51, 175–184 (2013)

    Google Scholar 

  15. Rahimi, G., Gazor, M., Hemmatnezhad, M., Toorani, H.: On the postbuckling and free vibrations of FG Timoshenko beams. Compos. Struct. 95, 247–253 (2013)

    Article  Google Scholar 

  16. Rajasekaran, S.: Free vibration of centrifugally stiffened axially functionally graded tapered Timoshenko beams using differential transformation and quadrature methods. Appl. Math. Model. 37, 4440–4463 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  17. Shahba, A., Attarnejad, R., Marvi, M., Hajilar, S.: Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions. Compos. B 42, 801–808 (2011)

    Article  Google Scholar 

  18. Şimşek, M.: Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load. Compos. Struct. 92, 2532–2546 (2010)

    Article  Google Scholar 

  19. Yesilce, Y., Demirdag, O.: Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems. Int. J. Mech. Sci. 50, 995–1003 (2008)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Tartu, Tartu, Estonia

    Ülo Lepik

  2. Institute of Computer Science, University of Tartu, Tartu, Estonia

    Helle Hein

Authors
  1. Ülo Lepik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Helle Hein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ülo Lepik .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Lepik, Ü., Hein, H. (2014). Vibrations of Functionally Graded Timoshenko Beams. In: Haar Wavelets. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-04295-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-04295-4_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04294-7

  • Online ISBN: 978-3-319-04295-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation