Аннотация
This research establishes a comprehensive mathematical and numerical framework for accurately predicting the resonant frequencies of fluid-filled thin-walled structures, a critical factor in the safety and performance of engineering systems such as storage tanks, pipelines, and aerospace components. The study addresses the inherent limitations of classical analytical solutions, which are typically restricted to idealized geometries and cannot account for the complexities of real-world applications. By coupling the Navier-Lamé equations for elastic shell motion with the Laplace equation for the fluid domain, the model effectively captures the "added mass effect"—the phenomenon where internal fluid interaction significantly reduces a structure's natural frequencies. This effect is particularly pronounced in systems with denser fluids, larger radii, and thinner walls. The proposed framework was rigorously validated against a diverse dataset of 54 experimental cases from peer-reviewed literature, covering various geometries (spheres, cylinders, and square plates) and materials including glass, steel, and aluminum. The results demonstrated exceptional reliability, with an average relative error of less than 0.5% across all tested configurations. Statistical analysis, including Boxplots and Empirical CDFs, further confirmed that the model maintains sub-percent-level accuracy, with 100% of cases showing less than 1.1% error. Implemented within the ANSYS finite element environment, the model's computational efficiency and high precision make it an ideal tool for integration into digital twin systems. Such integration enables real-time dynamic monitoring and predictive maintenance of complex industrial infrastructure. Future developments aim to enhance the model by incorporating nonlinear fluid effects, such as sloshing, and integrating these simulations into Industrial Internet of Things (IIoT) frameworks.