Mathematical and numerical modeling of resonant frequencies of fluid-structure systems for digital twins

This research establishes a comprehensive mathematical and numerical framework designed for the accurate prediction of resonant frequencies in fluid-filled thin-walled structures. Such predictions are critical for ensuring the safety and performance of various engineering systems, including storage tanks, pipelines, and aerospace components. The framework addresses the inherent limitations of classical analytical solutions, which are typically restricted to idealized geometries and often fail to account for the complexities encountered in real-world applications. By coupling the Navier-Lamé equations, which govern elastic shell motion, with the Laplace equation for the fluid domain, the model effectively captures the 'added mass effect.' This phenomenon, where internal fluid interaction significantly reduces a structure's natural frequencies, is

particularly pronounced in systems characterized by denser fluids, larger radii, and thinner walls. The proposed framework underwent rigorous validation against a diverse dataset comprising 54 experimental cases from peer-reviewed literature, encompassing various geometries such as spheres, cylinders, and square plates, and materials including glass, steel, and aluminum. The validation results demonstrated exceptional reliability, achieving an average relative error of less than 0.5% across all tested configurations. Further statistical analysis, utilizing tools such as Boxplots and Empirical Cumulative Distribution Functions (CDFs), confirmed the model's consistent sub-percent-level accuracy.

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