Abstract
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.
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Faruq Muhammad Foong is a Ph.D. student in the School of Mechanical Engineering, Heriot-Watt University, Putrajaya, Malaysia. He received his Bachelor of Aerospace Engineering degree (Hons) from Monash University, Australia. His research interests include energy harvesting, linear and non-linear vibrations.
C. K. Thein graduated from University of Hull, UK with a B.S. and Ph.D. in Mechanical Engineering in 2007 and 2011, respectively. He is currently an Assistant Professor at Heriot-Watt University Malaysia since 2016. His research interests include multiobjective and multi-disciplinary optimisation and vibration energy harvesting devices for wireless sensor network applications.
B. L. Ooi obtained a Master of engineering degree from the University of Hull, UK, in 2007 and Ph.D. in energy harvesting in 2011. In 2014, he joined Quest Inter-national University Perak (Malaysia) as a Lecturer. His research interest includes vibration energy harvesting devices for environmental sensing purposes.
A. Rashid A. Aziz received his B.S. in 1988, M.S. in 1990 and a Ph.D. in Mechanical Engineering from the University of Miami, USA, in 1995. He is currently a Professor and Head of Centre for Automotive Research and Electric Mobility (CAREM), Universiti-Teknologi PETRONAS. His research interests include internal combustion engines, fluid mechanics, computational fluid dynamics, heat transfer and alternative energy.
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Foong, F.M., Ket, T.C., Lee, O.B. et al. Stress and damping of wide cantilever beams under free vibration. J Mech Sci Technol 33, 21–27 (2019). https://doi.org/10.1007/s12206-018-1203-8
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DOI: https://doi.org/10.1007/s12206-018-1203-8