Journal of Mechanical Science and Technology

, Volume 33, Issue 1, pp 21–27 | Cite as

Stress and damping of wide cantilever beams under free vibration

  • Faruq Muhammad Foong
  • Thein Chung KetEmail author
  • Ooi Beng Lee
  • Abdul Rashid Abdul Aziz


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.


Damping Stress Wide cantilever beam Plate theory Beam theory 


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Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Faruq Muhammad Foong
    • 1
  • Thein Chung Ket
    • 1
    Email author
  • Ooi Beng Lee
    • 2
  • Abdul Rashid Abdul Aziz
    • 3
  1. 1.School of Engineering and Physical SciencesHeriot-Watt UniversityPrecinct 5Malaysia
  2. 2.Intel PSG, PG 14, Plot 6, Bayan Lepas TechnoplexMedan Bayan LepasPenangMalaysia
  3. 3.Center for Automotive Research and Electric Mobility (CAREM)Universiti Teknologi PETRONAS (UTP)TronohMalaysia

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