Free Vibration of Axially Functionally Graded Timoshenko Circular Arch


  • Joon Kyu Lee

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

  • Hee Min Yoon

    Saman Corporation, 13 Byeoryangsangga-ro, Gwacheon-si, Gyeonggi-do 13837, Republic of Korea

  • Sang Jin Oh

    Department of Civil and Environmental Engineering, Jeonnam State University, 152 Jookrokwon-ro, Damyang-eup, Damyang-gun, Jeonnam 57337, Republic of Korea

  • Byoung Koo Lee

    Department of Civil and Environmental Engineering, Wonkwang University, 460 Iksan-daero, Iksan, Jeonbuk 54538, Republic of Korea


Functionally graded materials are innovative composites of hybrid ceramics and metals that exhibit excellent mechanical performance in harsh temperature environments and under various external loads. In this study, the free vibrations of Timoshenko circular arches, made of functionally graded materials in the axial direction, are investigated. The material properties of Young's modulus and mass density of the arch vary according to a symmetric quadratic function along the arch axis. Differential equations governing the free vibration of the arch including the rotatory inertia and shear deformation, called the Timoshenko arch, are derived. A novel numerical solution method is developed to calculate the natural frequencies and mode shapes of the arch. Parametric studies of the modular ratio, shear correction factor, shear modulus ratio, and slenderness ratio on the natural frequencies are conducted, and the results are reported in the tables and figures.


free vibration, axially functionally graded material, Timoshenko arch, natural frequency, mode shape

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Published Online


How to Cite

Lee, J. K., Yoon, H. M., Oh, S. J., Lee, B. K. “Free Vibration of Axially Functionally Graded Timoshenko Circular Arch”, Periodica Polytechnica Civil Engineering, 68(2), pp. 445–458, 2024.



Research Article