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Free vibration analysis of beams with non-ideal clamped boundary conditions

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Abstract

A non-ideal boundary condition is modeled as a linear combination of the ideal simply supported and the ideal clamped boundary conditions with the weighting factors k and 1-k, respectively. The proposed non-ideal boundary model is applied to the free vibration analyses of Euler-Bernoulli beam and Timoshenko beam. The free vibration analysis of the Euler-Bernoulli beam is carried out analytically, and the pseudospectral method is employed to accommodate the non-ideal boundary conditions in the analysis of the free vibration of Timoshenko beam. For the free vibration with the non-ideal boundary condition at one end and the free boundary condition at the other end, the natural frequencies of the beam decrease as k increases. The free vibration where both the ends of a beam are restrained by the non-ideal boundary conditions is also considered. It is found that when the non-ideal boundary conditions are close to the ideal clamped boundary conditions the natural frequencies are reduced noticeably as k increases. When the non-ideal boundary conditions are close to the ideal simply supported boundary conditions, however, the natural frequencies hardly change as k varies, which indicate that the proposed boundary condition model is more suitable to the non-ideal boundary condition close to the ideal clamped boundary condition.

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Authors and Affiliations

  1. Department of Mechanical and Design Engineering, Hongik University, Jochiwon, Sejong, 339-701, Korea

    Jinhee Lee

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  1. Jinhee Lee
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Correspondence to Jinhee Lee.

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Recommended by Editor Yeon June Kang

Jinhee Lee received B.S. and M.S. degrees from Seoul National University and KAIST in 1982 and 1984, respectively. He received his Ph.D degree from University of Michigan, Ann Arbor in 1992 and joined Dept. of Mechanical and Design Engineering of Hongik University in Sejong, Korea. His research interests include inverse problems, pseudospectral method, vibration and dynamic systems.

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Lee, J. Free vibration analysis of beams with non-ideal clamped boundary conditions. J Mech Sci Technol 27, 297–303 (2013). https://doi.org/10.1007/s12206-012-1245-2

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  • DOI: https://doi.org/10.1007/s12206-012-1245-2

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