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Free vibrations of tapered beams laterally restrained by elastic springs

  • Structural Engineering
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KSCE Journal of Civil Engineering Aims and scope

Abstract

This paper discusses the development of numerical methods for calculating the natural frequencies of tapered beams that are laterally restrained by elastic springs. In formulating the governing equation of the beam, each elastic spring is modeled as a discrete Winkler foundation of the finite longitudinal length, and the effect of axial load is included. By using this model, the differential equation governing the free vibration of the beam is derived, which is solved numerically. The Runge-Kutta method is used to integrate the differential equation, and the determinant search method combined with the Regula-Falsi method is used to determine the eingenvalues, namely, the natural frequencies. In the numerical examples, clamped-clamped, clamped-hinged, hinged-clamped and hinged-hinged end constraints are considered. The numerical results, including the frequency parameters and mode shapes of free vibrations are presented in non-dimensional forms.

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Authors and Affiliations

  1. Department of Civil & Environmental Engineering, Wonkwang University, 570-749, Iksan, Junbuk, Korea

    Byoung-Koo Lee (Member, Professor)

  2. Department of Civil & Environmental Engineering, Dankook University, 330-714, Chonan, Chungnam, Korea

    Suk-Ki Kim (Member, Professor)

  3. Wonkwang University, Iksan, Korea

    Tae-Eun Lee (Member, Graduate Student) & Dae-Soon Ahn

Authors
  1. Byoung-Koo Lee
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  2. Suk-Ki Kim
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  3. Tae-Eun Lee
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  4. Dae-Soon Ahn
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Additional information

The manuscript for this paper was submitted for review on December 23, 2002.

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Lee, BK., Kim, SK., Lee, TE. et al. Free vibrations of tapered beams laterally restrained by elastic springs. KSCE J Civ Eng 7, 193–199 (2003). https://doi.org/10.1007/BF02841975

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  • DOI: https://doi.org/10.1007/BF02841975

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