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Free vibration analysis of functionally graded beams using complementary functions method

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Abstract

A novel approach is employed in the free vibration analysis of simply supported functionally graded beams. Modulus of elasticity, density of material, and Poisson’s ratio may change arbitrarily in the thickness direction. The equations of motion are derived using the plane elasticity theory. The governing differential equations have variable coefficients, which are functions of material properties. Analytical solutions of such equations are limited to specific material properties. Hence, numerical approaches must be adopted to solve the problem on hand. The complementary functions method will be infused into the analysis to convert the problem into an initial-value problem which can be solved accurately. Solutions thus obtained are compared to closed-form benchmark solutions available in the literature and finite element software solutions to validate the method presented. Subsequently, it is demonstrated that the method is efficiently applicable to material properties changing arbitrarily through the thickness with continuous derivatives.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Adana Science and Technology University, 01180, Adana, Turkey

    Kerimcan Celebi

  2. Department of Mathematics, Osmaniye Korkut Ata University, 80000, Osmaniye, Turkey

    Durmus Yarimpabuc

  3. Department of Mechanical Engineering, Çukurova University, 01330, Adana, Turkey

    Naki Tutuncu

Authors
  1. Kerimcan Celebi
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  2. Durmus Yarimpabuc
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  3. Naki Tutuncu
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Correspondence to Kerimcan Celebi.

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Celebi, K., Yarimpabuc, D. & Tutuncu, N. Free vibration analysis of functionally graded beams using complementary functions method. Arch Appl Mech 88, 729–739 (2018). https://doi.org/10.1007/s00419-017-1338-6

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  • DOI: https://doi.org/10.1007/s00419-017-1338-6

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