Natural frequencies of composite cylindrical shells under uncertainty: a nonparametric approach

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© The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering 2025.Uncertainty in the natural frequencies of composite cylindrical shells is typically assessed with parametric models that assume specific probability laws for material and geometric inputs. Here, we propose a fully data-driven, nonparametric alternative based on the orthogonal bootstrap, integrated into a semi-analytical Rayleigh–Ritz framework for shells subjected to axial load and internal pressure. This study makes four key contributions: (1) It introduces the orthogonal bootstrap to the structural dynamics of composite shells, enabling uncertainty propagation directly from empirical samples without prescribing distributions; (2) it provides a head-to-head comparison between the nonparametric approach and a conventional parametric Monte Carlo scheme (Beta-distributed), clarifying the conditions under which each method is most advantageous; (3) it incorporates stress-stiffening effects (geometric stiffness) from axial compression and internal pressure into the Rayleigh–Ritz formulation, enabling probabilistic frequency estimates under combined loading; and (4) it validates the semi-analytical results against a refined finite-element model, demonstrating an order-of-magnitude reduction in computational time with orthogonal resampling. The results reveal that frequency variability is primarily dominated by the radius-to-thickness ratio and fiber elastic modulus, while density predominantly influences mass-driven shifts. The proposed framework offers a transparent, efficient means of quantifying uncertainty in composite shell dynamics without the risk of distributional misspecification, and it can be readily extended to other laminated configurations and loading scenarios.

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