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Purpose <p>This study investigates the multimodal propagation of bending waves in functionally graded material (FGM) beams under intrinsic uncertainties in material and geometric properties. The objective is to quantify their effects on propagation constants and the dispersive behavior of the structure.</p> Methods <p>A hybrid stochastic framework combining the Wave Finite Element (WFE) method and probabilistic analysis is developed. Stiffness and mass matrices are derived analytically using Euler–Bernoulli beam theory, capturing bending, shear, and rotational modes with their couplings. These matrices are embedded into the WFE formulation to characterize dispersion curves of a periodic unit cell. Uncertainties are modeled as Gaussian random variables and propagated through Monte Carlo simulations. A stochastic analytical formulation is further introduced to validate numerical predictions.</p> Results <p>The approach quantifies the variability of dispersion curves, revealing high sensitivity to uncertain input parameters. Both Gaussian and lognormal distributions provide consistent results under moderate variability. The Gaussian model offers sufficient accuracy and simplicity, while the lognormal is theoretically better suited for strictly positive parameters. Monte Carlo simulations, although computationally demanding, remain reliable for validation, while polynomial chaos and stochastic collocation methods enable efficient large-scale analysis.</p> Conclusion <p>The proposed stochastic WFE framework effectively characterizes the influence of uncertainties on wave propagation in FGM beams. The results highlight the importance of uncertainty quantification in dispersion studies and demonstrate a balance between computational efficiency and predictive accuracy using complementary stochastic techniques.</p>

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Bending Vibration in Uncertain Function Gradient Material Structure Through Stochastic Wave Finite Element Method

  • 期刊论文

  • 发表日期：

    2025年9月28日

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  • Mokhtar Juini,
  • Henia Arfa,
  • Faker Bouchoucha,
  • Issam Abed,
  • Mohamed Ichchou

摘要

Purpose

This study investigates the multimodal propagation of bending waves in functionally graded material (FGM) beams under intrinsic uncertainties in material and geometric properties. The objective is to quantify their effects on propagation constants and the dispersive behavior of the structure.

Methods

A hybrid stochastic framework combining the Wave Finite Element (WFE) method and probabilistic analysis is developed. Stiffness and mass matrices are derived analytically using Euler–Bernoulli beam theory, capturing bending, shear, and rotational modes with their couplings. These matrices are embedded into the WFE formulation to characterize dispersion curves of a periodic unit cell. Uncertainties are modeled as Gaussian random variables and propagated through Monte Carlo simulations. A stochastic analytical formulation is further introduced to validate numerical predictions.

Results

The approach quantifies the variability of dispersion curves, revealing high sensitivity to uncertain input parameters. Both Gaussian and lognormal distributions provide consistent results under moderate variability. The Gaussian model offers sufficient accuracy and simplicity, while the lognormal is theoretically better suited for strictly positive parameters. Monte Carlo simulations, although computationally demanding, remain reliable for validation, while polynomial chaos and stochastic collocation methods enable efficient large-scale analysis.

Conclusion

The proposed stochastic WFE framework effectively characterizes the influence of uncertainties on wave propagation in FGM beams. The results highlight the importance of uncertainty quantification in dispersion studies and demonstrate a balance between computational efficiency and predictive accuracy using complementary stochastic techniques.