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Free Vibration Analysis of Axially Functionally Graded (AFG) Cantilever Columns of a Regular Polygon Cross-Section with Constant Volume

Author

Listed:
  • Joon Kyu Lee

    (Department of Civil Engineering, University of Seoul, 163 Seoulsiripdae-ro, Dongdaemun-gu, Seoul 02504, Korea)

  • Byoung Koo Lee

    (Department of Civil and Environmental Engineering, Wonkwang University, 460 Iksan-daero, Iksan-si, Jeollabuk-do 54538, Korea)

Abstract

This paper deals with the transverse free vibration of axially functionally graded (AFG) cantilever columns under the influence of axial compressive load. The columns possessing a regular polygon in their cross-section are tapered and their material properties vary along the axis of the column. An emphasis is placed on the columns with constant volume for admissible geometries and materials. The governing differential equation of the problem is derived and solved using the direct integral approach in conjunction with the determinant search technique. The obtained results are in good agreement with those in the available literature and computed by finite element analysis. Numerical examples for the natural frequency and mode shape of the columns are presented to investigate the effects of parameters related to geometrical nonuniformity and material inhomogeneity.

Suggested Citation

  • Joon Kyu Lee & Byoung Koo Lee, 2020. "Free Vibration Analysis of Axially Functionally Graded (AFG) Cantilever Columns of a Regular Polygon Cross-Section with Constant Volume," Mathematics, MDPI, vol. 8(3), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:319-:d:326745
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    References listed on IDEAS

    as
    1. Yasin Yilmaz & Zekeriya Girgin & Savas Evran, 2013. "Buckling Analyses of Axially Functionally Graded Nonuniform Columns with Elastic Restraint Using a Localized Differential Quadrature Method," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-12, July.
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