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The natural vibration characteristics of beams composed by functionally graded materials are here studied by means of the dynamic stiffness method. The equations of motion and boundary conditions for free vibration of Euler-Bernoulli beams, in which the material properties vary smoothly across the thickness with a symmetric law, are derived. The Wittrick and Williams algorithm is applied to the dynamic stiffness matrix to identify natural frequencies and vibration modes. A parametric study is conducted by varying the beam’s geometry and the mechanical properties of the graded material.

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Free Vibrations of Symmetric Functionally Graded Beams

  • 会议论文

  • 发表日期：

    2026年

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  • Lorenzo Ledda,
  • Annalisa Greco,
  • Ilaria Fiore,
  • Ivo Caliò

摘要

The natural vibration characteristics of beams composed by functionally graded materials are here studied by means of the dynamic stiffness method. The equations of motion and boundary conditions for free vibration of Euler-Bernoulli beams, in which the material properties vary smoothly across the thickness with a symmetric law, are derived. The Wittrick and Williams algorithm is applied to the dynamic stiffness matrix to identify natural frequencies and vibration modes. A parametric study is conducted by varying the beam’s geometry and the mechanical properties of the graded material.