Analytical Study on Free Vibration Dynamics of Compressible Fluids in Rigid-Walled Rectangular Tanks

This paper presents a comprehensive analytical study on the free vibration dynamics of compressible fluids within rigid-walled rectangular tanks, emphasizing the significance of fluid-structure interaction (FSI). The research derives the governing partial differential equations and boundary conditions, leading to exact solutions for two-dimensional and three-dimensional tank geometries. By employing the Rayleigh-Ritz method, the study incorporates the effects of fluid compressibility, offering a robust framework for analyzing the free vibration behavior. The paper calculates the natural frequencies through derived analytical expressions and examines the impact of varying tank dimensions (length, height, and width) on these frequencies via sensitivity analyses. Results reveal a consistent decrease in natural frequencies across all modes as the length, height, or width of the tank increases. This phenomenon is attributed to the interplay between the fluid's kinetic and potential energies, governed by the compressibility effects and the available space for wave formation within the larger tanks. The analytical approach, combined with the Rayleigh-Ritz method, provides a solid foundation for understanding FSI in engineering applications involving storage tanks and seismic-resistant structures. The study offers valuable insights into the significance of FSI considerations and highlights the importance of optimizing tank dimensions to achieve desired resonance characteristics, ensuring safe and efficient operation under various loading conditions.