Breathing Vibrations of a Partially Filled Cylindrical Tank—Linear Theory

Abstract

An accurate linear hydrodynamic theory (incompressible) is presented for breathing vibrations of a liquid column with an assumed mode shape. It yields the natural frequencies of liquid sloshing as well as the pressure distribution. A simplified frequency prediction for the partially filled cylindrical shell is derived from the Donnell-Yu equation with an apparent mass correction. Comparison with some available experiments show good agreement for breathing vibrations with the fundamental longitudinal mode.