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

Abstract

This paper calculates the natural frequencies using analytical expressions derived from the Helmholtz equation, with boundary conditions adapted for rigid-walled rectangular tanks. These analytical methods facilitate the examination of how variations in tank dimensions (length, height, and width) influence the frequencies via sensitivity analysis. Results indicate that increases in the length, height, or width of the tank consistently result in a decrease in natural frequencies across all modes. This foundational study advances the understanding of fluid-structure interaction (FSI) in engineering applications such as storage tanks and seismic-resistant structures and provides valuable insights for future research