Stress and damping of wide cantilever beams under free vibration

Faruq Muhammad Foong, Thein Chung Ket*, Ooi Beng Lee, Abdul Rashid Abdul Aziz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Research has shown that the damping of a vibrating structure is highly dependent on its stress function. In this study, the bending stress and damping of wide cantilever beams under free vibration were analyzed using the classical plate and beam theory. The damping stress equation for cantilever beams under free vibration was derived based on the empirical function of unit dissipating energy, whereas the plate bending equation was derived using the double finite integral transform method. The bending stress and damping ratio results from the beam and the plate theory were compared with simulation results from finite element analysis (FEA) for different length-to-width ratios. Results show that the plate theory displayed a good agreement with FEA results in terms of estimated value and trending curve shape when a significantly large number of terms were used. Using a small number of terms resulted in large errors at high length-to-width ratios, but provided sufficient estimates when the length-to-width ratio dropped below four. It was found that the beam theory was only valid for beams with very high length-to-width ratios or square plates. Beyond this ratio, the beam theory recorded a higher error estimate than the plate theory. Overall, the most accurate stress and damping estimations come from the use of plate theory with a very high number of terms.

Original languageEnglish
Pages (from-to)21-27
Number of pages7
JournalJournal of Mechanical Science and Technology
Issue number1
Early online date14 Jan 2019
Publication statusPublished - Jan 2019


  • Beam theory
  • Damping
  • Plate theory
  • Stress
  • Wide cantilever beam

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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