Skip to main content

Advertisement

SpringerLink
Log in

Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

This study presents free vibration analysis of rotating functionally graded Timoshenko beam made of porous material using the semi-analytical differential transform method.The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. The frequency equation is obtained using Hamilton’s principle. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of porous FG rotating beams. The good agreement between the results of this article and those available in literature validated the presented approach. Detailed mathematical derivations are presented and numerical investigations are performed, while emphasis is placed on investigating the effect of the several parameters such as porosity, functionally graded microstructure, thickness ratio, rotational speed and hub radius on the normalized natural frequencies of porous FG rotating beams in detail.

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

Similar content being viewed by others

References

  1. Abdel-Halim Hassan IH (2002) On solving some eigenvalue problems by using a differential transformation. Appl Math Comput 127(1):1–22

    Article  MathSciNet  MATH  Google Scholar 

  2. Banerjee JR (2001) Dynamic stiffness formulation and free vibration analysis of centrifugally stiffened Timoshenko beams. J Sound Vib 247(1):97–115

    Article  Google Scholar 

  3. Ebrahimi F (2013) Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment. Mech Adv Mater Struct 20(10):854–870

    Article  MathSciNet  Google Scholar 

  4. Ebrahimi F, Rastgoo A, Atai AA (2009) A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate. Eur J Mech A Solids 28(5):962–973

    Article  Google Scholar 

  5. Ebrahimi F, Naei MH, Rastgoo A (2009) Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation. J Mech Sci Technol 23(8):2107–2124

    Article  Google Scholar 

  6. Ho SH, Chen COK (2006) Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform. Int J Mech Sci 48(11):1323–1331

    Article  MATH  Google Scholar 

  7. Hodges DY, Rutkowski MY (1981) Free-vibration analysis of rotating beams by a variable-order finite-element method. AIAA J 19(11):1459–1466

    Article  MATH  Google Scholar 

  8. Mei C (2008) Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam. Comput Struct 86(11):1280–1284

    Article  Google Scholar 

  9. Şimşek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des 240(4):697–705

    Article  Google Scholar 

  10. Wattanasakulpong N, Ungbhakorn V (2014) Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerosp Sci Technol 32(1):111–120

    Article  Google Scholar 

  11. Wattanasakulpong N, Gangadhara Prusty B, Kelly DW, Hoffman M (2012) Free vibration analysis of layered functionally graded beams with experimental validation. Mater Des 36:182–190

    Article  Google Scholar 

  12. Zhou JK (1986) Differential transformation and its applications for electrical circuits. Huazhong University Press, Wuhan, China

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, P.O.B. 16818-34149, Qazvin, Iran

    Farzad Ebrahimi & Mohadese Mokhtari

Authors
  1. Farzad Ebrahimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohadese Mokhtari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farzad Ebrahimi.

Additional information

Technical Editor: Fernando Alves Rochinha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ebrahimi, F., Mokhtari, M. Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method. J Braz. Soc. Mech. Sci. Eng. 37, 1435–1444 (2015). https://doi.org/10.1007/s40430-014-0255-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-014-0255-7

Keywords

Search

Navigation