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<p>Laminated composite beams are critical components in advanced engineering systems, yet their performance is invariably affected by inherent uncertainties in material properties, geometric parameters, and operational loads. Conventional deterministic models, despite their sophistication, fail to account for these stochastic factors, fundamentally limiting predictive accuracy and impeding the development of robust designs. To overcome this limitation, a comprehensive probabilistic framework is essential for characterizing the stochastic nonlinear dynamics of these structures. This paper establishes a novel probability density evolution framework to address this challenge. The dynamic model is formulated using the First-Order Shear Deformation Theory (FSDT) coupled with von Kármán geometric nonlinearity to accurately capture the beam’s behavior. The primary contribution of this work is the rigorous derivation of the Fokker–Planck–Kolmogorov (FPK) equation, which governs the temporal evolution of the joint probability density function of the system’s response. To the best of our knowledge, this is the first study to formulate the FPK equation for this class of nonlinear laminated beams. To solve the resulting high-dimensional FPK equation, an efficient and accurate numerical solver based on a Radial Basis Function Neural Network (RBFNN) is employed. This integrated FPK–RBFNN approach provides a complete probabilistic characterization of the system’s dynamics with significantly greater computational efficiency than traditional Monte Carlo simulations (MCS). A systematic sensitivity analysis was conducted to investigate the stochastic nonlinear response of the beam under random excitation. The results reveal that response variability is dominated by macro-scale uncertainties, whereas micro-scale manufacturing imperfections have a comparatively minor influence. Furthermore, ply reorientation and ply count reduction were identified as effective strategies for vibration suppression. Notably, a significant synergistic effect was discovered when these two strategies were combined, yielding a reduction in vibration response greater than the sum of their individual effects. The accuracy and efficiency of the proposed framework are rigorously validated against MCS.</p>

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A probabilistic framework for stochastic dynamic response of composite laminated beams with geometrical nonlinearity

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Jiamin Qian,
  • Lincong Chen,
  • Yegao Qu

摘要

Laminated composite beams are critical components in advanced engineering systems, yet their performance is invariably affected by inherent uncertainties in material properties, geometric parameters, and operational loads. Conventional deterministic models, despite their sophistication, fail to account for these stochastic factors, fundamentally limiting predictive accuracy and impeding the development of robust designs. To overcome this limitation, a comprehensive probabilistic framework is essential for characterizing the stochastic nonlinear dynamics of these structures. This paper establishes a novel probability density evolution framework to address this challenge. The dynamic model is formulated using the First-Order Shear Deformation Theory (FSDT) coupled with von Kármán geometric nonlinearity to accurately capture the beam’s behavior. The primary contribution of this work is the rigorous derivation of the Fokker–Planck–Kolmogorov (FPK) equation, which governs the temporal evolution of the joint probability density function of the system’s response. To the best of our knowledge, this is the first study to formulate the FPK equation for this class of nonlinear laminated beams. To solve the resulting high-dimensional FPK equation, an efficient and accurate numerical solver based on a Radial Basis Function Neural Network (RBFNN) is employed. This integrated FPK–RBFNN approach provides a complete probabilistic characterization of the system’s dynamics with significantly greater computational efficiency than traditional Monte Carlo simulations (MCS). A systematic sensitivity analysis was conducted to investigate the stochastic nonlinear response of the beam under random excitation. The results reveal that response variability is dominated by macro-scale uncertainties, whereas micro-scale manufacturing imperfections have a comparatively minor influence. Furthermore, ply reorientation and ply count reduction were identified as effective strategies for vibration suppression. Notably, a significant synergistic effect was discovered when these two strategies were combined, yielding a reduction in vibration response greater than the sum of their individual effects. The accuracy and efficiency of the proposed framework are rigorously validated against MCS.