Free vibration analysis of functionally graded Euler-Bernoulli and Timoshenko beams using Levy-type solution

Luan C Trinh, Adelaja Israel Osofero* (Corresponding Author), Thuc P Vo, Trung-Kien Nguyen

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingPublished conference contribution


In this paper, fundamental frequency of Functionally Graded (FG) beams with various boundary conditions is presented based on Classical Beam Theory (CBT) and First-order Beam Theory (FOBT). The material properties that vary across the thickness are determined by the power law. Governing equations of motion and boundary conditions are derived from the Hamilton’s principle. Levy-type solution is applied to analyse the effect of span-to-thickness ratio, power-law index and boundary conditions on the vibration behaviour of FG beams. Present results show that natural frequency decreases with an increase in power-law index and a decrease in span-to-thickness ratio. This work also corroborates the suggestion that the shear effect should be considered in studying natural vibration of FG moderate thick beams, especially for Clamped-Clamped or Clamped-Simply Support boundary conditions.
Original languageEnglish
Title of host publication2nd International Conference on Agriculture, Biotechnology, Science and Engineering (iCABSE 2015)
PublisherAENSI Publisher
Number of pages7
Publication statusPublished - 28 Aug 2015
EventICABSE 2015 - Ho Chi Minh City, Viet Nam
Duration: 28 Aug 201529 Aug 2015


ConferenceICABSE 2015
Country/TerritoryViet Nam
CityHo Chi Minh City

Bibliographical note

Mr Luan C. Trinh is supported by Northumbria
University Research Development Fund.


  • Functionally Graded (FG) beam
  • Free vibration
  • Levy-type solution
  • Arbitrary boundary conditions


Dive into the research topics of 'Free vibration analysis of functionally graded Euler-Bernoulli and Timoshenko beams using Levy-type solution'. Together they form a unique fingerprint.

Cite this