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An Analytical Approach to Vibration Analysis of Beams with Variable Properties

  • Research Article - Civil Engineering
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Abstract

In this paper, an approach is proposed for determination of vibration frequencies of variable cross-section Timoshenko beams and of non-prismatic Euler beams under variable axial loads. In each case, the governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single-variable equation in terms of location. Integral equations for the weak form of governing equations are derived through repetitive integrations. Mode shape functions are approximated by a power series. A system of linear algebraic equations is obtained by substitution of the power series into the integral equation. Using a non-trivial solution for system of equations, natural frequencies are determined. The presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic Euler beams. The effectiveness and accuracy of the method is shown through comparison of the numerical results to those obtained using available finite element software.

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Authors and Affiliations

  1. Department of Civil Engineering, Birjand University of Technology, Birjand, Iran

    M. Mohammadnejad

  2. Department of Civil Engineering, Shahid Bahonar University of Kerman, PO Box 76169-133, Kerman, Iran

    H. Saffari & M. H. Bagheripour

Authors
  1. M. Mohammadnejad
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  2. H. Saffari
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  3. M. H. Bagheripour
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Correspondence to H. Saffari.

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Mohammadnejad, M., Saffari, H. & Bagheripour, M.H. An Analytical Approach to Vibration Analysis of Beams with Variable Properties. Arab J Sci Eng 39, 2561–2572 (2014). https://doi.org/10.1007/s13369-013-0898-1

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  • DOI: https://doi.org/10.1007/s13369-013-0898-1

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