Spectral Properties of Mimetic Operators for Robust Fluid–Structure Interaction in the Design of Aircraft Wings
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2024-04-18Estado
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. This paper presents a comprehensive study on the spectral properties of mimetic finitedifference operators and their application in the robust fluid–structure interaction (FSI) analysis of
aircraft wings under uncertain operating conditions. By delving into the eigenvalue behavior of
mimetic Laplacian operators and extending the analysis to stochastic settings, we develop a novel
stochastic mimetic framework tailored for addressing uncertainties inherent in the fluid dynamics
and structural mechanics of aircraft wings. The framework integrates random matrix theory with
mimetic discretization methods, enabling the incorporation of uncertainties in fluid properties,
structural parameters, and coupling conditions at the fluid–structure interface. Through spectral
and localization analysis of the coupled stochastic mimetic operator, we assess the system’s stability,
sensitivity to perturbations, and computational efficiency. Our results highlight the potential of
the stochastic mimetic approach for enhancing reliability and robustness in the design of aircraft
wings, paving the way for optimization algorithms that integrate uncertainties directly into the
design process. Our findings reveal a significant impact of stochastic perturbations on the spectral
radius and eigenfunction localization, indicating heightened system sensitivity. The introduction
of randomized singular value decomposition (RSVD) within our framework not only enhances
computational efficiency but also preserves accuracy in low-rank approximations, which is critical
for handling large-scale systems. Moreover, Monte Carlo simulations validate the robustness of
our stochastic mimetic framework, showcasing its efficacy in capturing the nuanced dynamics of
FSI under uncertainty. This study contributes to the fields of numerical methods and aerospace
engineering by offering a rigorous and scalable approach for conducting uncertainty-aware FSI
analysis, which is crucial for the development of safer and more efficient aircraft.
Spectral Properties of Mimetic Operators for Robust Fluid–Structure Interaction in the Design of Aircraft Wings
Tipo de Actividad
Artículos en revistasISSN
2227-7390Palabras Clave
.mimetic finite-difference operators; spectral analysis; stochastic analysis; aircraft wing