Journal of Engineering Mathematics

, Volume 80, Issue 1, pp 91–104 | Cite as

Higher-order theory for bending and vibration of beams with circular cross section

  • Y. Huang
  • J. X. Wu
  • X. F. LiEmail author
  • L. E. Yang


This paper presents an efficient and simple higher-order theory for analyzing free vibration of cylindrical beams with circular cross section where the rotary inertia and shear deformation are taken into account simultaneously. Unlike the Timoshenko theory of beams, the present method does not require a shear correction factor. Similar to the Levinson theory for rectangular beams, this new model is a higher-order theory for beams with circular cross section. For transverse flexure of such cylindrical beams, based on the traction-free condition at the circumferential surface of the cylinder, two coupled governing equations for the deflection and rotation angle are first derived and then combined to yield a single governing equation. In the case of no warping of the cross section, our results are exact. A comparison is made of the natural frequencies with those using the Timoshenko and Euler–Bernoulli theories of beams and the finite element method. Our results are useful for precisely understanding the mechanical behavior and engineering design of circular cylindrical beams.


Beam of circular cross section Higher-order theory  Free vibration Natural frequency Timoshenko beam 



This work was supported by the TianYuan Special Funds of the National Natural Science Foundation of China (Grant Nos. 11126340 and 11226303).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsFoshan UniversityFoshanChina
  2. 2.School of Civil EngineeringCentral South UniversityChangshaChina

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