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<p>A discrete mechanical model for large-amplitude free vibrations of two-stepped functionally graded beams is developed in this study. The beam’s material properties vary through the thickness according to a power-law distribution between the metallic and ceramic phases. The continuous beam is replaced by an N-degree-of-freedom system of lumped masses, longitudinal, and torsional springs. Using Hamilton’s principle, the governing nonlinear algebraic equations are derived and solved through the single-mode approach (SMA) to obtain the nonlinear frequency-amplitude relationships. In addition, an Artificial Neural Network (ANN)-based surrogate model is proposed to provide fast and accurate predictions of the nonlinear-to-linear frequency ratio as a function of key parameters such as step ratio, step position, boundary conditions, and the power-law index. Trained on data generated by the discrete formulation, the surrogate attains excellent generalization with a drastic reduction in computation time. The combined discrete-ANN framework offers both physical interpretability and computational efficiency, making it suitable for rapid design and optimization of complex FGM beam structures.</p>

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Deep neural network-based surrogate modeling for nonlinear vibrations of functionally graded stepped beams informed by a discrete model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月15日

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  • Anass Moukhliss,
  • Elmahdi Ezzoubaidi,
  • Nassima Ayoub,
  • abdellah Amouch,
  • ihsane tikonab,
  • Mohcine Chajdi,
  • Abdellatif Rahmouni,
  • Rhali Benamar

摘要

A discrete mechanical model for large-amplitude free vibrations of two-stepped functionally graded beams is developed in this study. The beam’s material properties vary through the thickness according to a power-law distribution between the metallic and ceramic phases. The continuous beam is replaced by an N-degree-of-freedom system of lumped masses, longitudinal, and torsional springs. Using Hamilton’s principle, the governing nonlinear algebraic equations are derived and solved through the single-mode approach (SMA) to obtain the nonlinear frequency-amplitude relationships. In addition, an Artificial Neural Network (ANN)-based surrogate model is proposed to provide fast and accurate predictions of the nonlinear-to-linear frequency ratio as a function of key parameters such as step ratio, step position, boundary conditions, and the power-law index. Trained on data generated by the discrete formulation, the surrogate attains excellent generalization with a drastic reduction in computation time. The combined discrete-ANN framework offers both physical interpretability and computational efficiency, making it suitable for rapid design and optimization of complex FGM beam structures.